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Posted on Jan 02, 2017

SOURCE: analytic geometry

assuming the question is what is the circle equation?

and if (-2,2) is the center of the circle

the equation should look like this: (x+2)^2+(Y-2)^2=R^2

And now only R is needed.

given 2x-5y+4=0 equation of line perpendicular

we can rearange the equation to be y=(2x+4)/5

from that we can see that the slope of the line is 2/5

And from the fact of perpendicular line we can say that the slope

of the radius line is -2/5.

The motivation now is to calculate the distance between the center of the circle to the cross point of the radius with the line perpendicular

For that we would calculate the radius line equation and compare it to the equation of line perpendicular

As mentioned earlier the slope of the radious line is -2/5.

So the equation is y=-2/5x+b and b can be calculated by using the center of the circle coordinates

2= - (2/5)*(-2)+b ------> b=2-4/5=1.2

radius equation is y=-(2/5)x+1.2

Now the cross point is calculated by comparing the equations:

-(2/5)x+1.2=(2x+4)/5 --> -2x+6=2x+4 --> 4x=2 --> x=1/2 --> y=1

So the cross point is (1/2,1).

The distance between the points is calculated by the following

Formula:

R=SQR(((1/2)-(-2))^2+(2-1)^2)=SQR(2.5^2+1^2)=SQR(6.25+1)=

SQR(7.25)

Therefore the circle eq is (x+2)^2+(Y-2)^2=7.25

Posted on Dec 15, 2008

that sounds like a problem about "slopes" so I am looking at using the derivative, which is basically the slope of the graph.

- the equation of line PQ can be simplified to y(x) = -2kx + k -8

- derivative relative to X (k is a constant) gives you -2k

- derivative of y(x) = 4x + 7 relative to x gives you 4

if the lines are parallel then the slopes are equal:

-2k=4 gives you k = -2 => your function becomes y = 4x - 8

if the lines are perpendicular the two slopes multiplied together give you -1:

-2k * 4 = -1 gives you k=1/8 => function becomes y = -1/4x - 7/8 or in other words y = -(2x+7)/8

I have made graphic representation and it looks to be correct.

I hope it makes sense.

- the equation of line PQ can be simplified to y(x) = -2kx + k -8

- derivative relative to X (k is a constant) gives you -2k

- derivative of y(x) = 4x + 7 relative to x gives you 4

if the lines are parallel then the slopes are equal:

-2k=4 gives you k = -2 => your function becomes y = 4x - 8

if the lines are perpendicular the two slopes multiplied together give you -1:

-2k * 4 = -1 gives you k=1/8 => function becomes y = -1/4x - 7/8 or in other words y = -(2x+7)/8

I have made graphic representation and it looks to be correct.

I hope it makes sense.

Apr 12, 2017 | Homework

Let's break this down into a few parts first.

Slope intercept form is otherwise known as y = mx + b, where m is the slope and b is the y-intercept.

Perpendicular means that the two lines will intersect each other at a 90 degree angle. In math terms, their slopes will be negative reciprocals of each other.

Starting with y + 4 = 1/4(x -7), putting into slope intercept form, y = mx + b, m = 1/4 and b=-7/4 -4.

Since it is perpendicular, it must have a slope that is a negative reciprocal. The slope of the original line is 1/4, so the multiplying it -1, we get -1/4, and taking the reciprocal, we get -4. So the slope of the perpendicular line is -4.

So, y = -4x + b, but we don't know what the value of b is. To determine this, we know the point (-4,7) is on the line that we are trying to find, so we can substitute it into the equation and calculate b to make it work.

Every time we see an x we put in -4 and every time we see a y, we put in 7.

y = -4x + b

7 = -4(-4) + b

7 = 16 + b

subtract 16 from both sides

7 - 16 = 16 + b - 16

-9 = b

Now substitute this into the equation.

y = -4x + -9

Putting it into correct form, we get y = -4x - 9.

Let's check it to see if it is correct.

It has a slope of -4, so it is perpendicular to y=1/4x - 5 3/4.

Is the point (-4,7) on the line? Let's substitute it in to see if it is on the line.

Again, everywhere we see an x, we put in -4 and everywhere we see a y we put in 7.

y= -4x - 9

7 = -4 (-4) - 9

7 = 16 - 9

7 = 7

Sorry for the very long explanation, I was being overly thorough, but after you do a few of them, you will be able to knock them off in minutes.

Good luck,

Paul

Slope intercept form is otherwise known as y = mx + b, where m is the slope and b is the y-intercept.

Perpendicular means that the two lines will intersect each other at a 90 degree angle. In math terms, their slopes will be negative reciprocals of each other.

Starting with y + 4 = 1/4(x -7), putting into slope intercept form, y = mx + b, m = 1/4 and b=-7/4 -4.

Since it is perpendicular, it must have a slope that is a negative reciprocal. The slope of the original line is 1/4, so the multiplying it -1, we get -1/4, and taking the reciprocal, we get -4. So the slope of the perpendicular line is -4.

So, y = -4x + b, but we don't know what the value of b is. To determine this, we know the point (-4,7) is on the line that we are trying to find, so we can substitute it into the equation and calculate b to make it work.

Every time we see an x we put in -4 and every time we see a y, we put in 7.

y = -4x + b

7 = -4(-4) + b

7 = 16 + b

subtract 16 from both sides

7 - 16 = 16 + b - 16

-9 = b

Now substitute this into the equation.

y = -4x + -9

Putting it into correct form, we get y = -4x - 9.

Let's check it to see if it is correct.

It has a slope of -4, so it is perpendicular to y=1/4x - 5 3/4.

Is the point (-4,7) on the line? Let's substitute it in to see if it is on the line.

Again, everywhere we see an x, we put in -4 and everywhere we see a y we put in 7.

y= -4x - 9

7 = -4 (-4) - 9

7 = 16 - 9

7 = 7

Sorry for the very long explanation, I was being overly thorough, but after you do a few of them, you will be able to knock them off in minutes.

Good luck,

Paul

Apr 03, 2016 | Office Equipment & Supplies

1) 2x + 5y = 7

2) 3x + 6y = 3

I'm going to use the method of elimination to solve for x and y.

Multiply 1) by 3 and 2) by 2 to allow the x's to be eliminated.

1) 6x + 15y = 21

2) 6x + 12y = 6

Now subtract line 2 from line 1.

0x + 3y = 15

---- ----

3 3 divide both sides by 3 to get y by itself.

y =5.

Substitute into 1) to calculate x.

2x + 5(5) = 7

2x + 25 = 7

2x + 25 -25 = 7 - 25

2x = -18

---- ----- divide both sides by 2 to get x by itself

2 2

x = -9

Check by plugging in answer into the other equation, in this case 2)

3 (-9) + 6(5) = 3

-27 + 30 = 3

3 = 3

We did it correctly and checked to prove that we did it right.

Good luck.

Paul

2) 3x + 6y = 3

I'm going to use the method of elimination to solve for x and y.

Multiply 1) by 3 and 2) by 2 to allow the x's to be eliminated.

1) 6x + 15y = 21

2) 6x + 12y = 6

Now subtract line 2 from line 1.

0x + 3y = 15

---- ----

3 3 divide both sides by 3 to get y by itself.

y =5.

Substitute into 1) to calculate x.

2x + 5(5) = 7

2x + 25 = 7

2x + 25 -25 = 7 - 25

2x = -18

---- ----- divide both sides by 2 to get x by itself

2 2

x = -9

Check by plugging in answer into the other equation, in this case 2)

3 (-9) + 6(5) = 3

-27 + 30 = 3

3 = 3

We did it correctly and checked to prove that we did it right.

Good luck.

Paul

Mar 12, 2015 | Office Equipment & Supplies

First, I graphed the lines and the point using Desmos.com.

I noticed that the two lines are perpendicular to each other and the point (1,-1) appears to be on the right side of the circle, on a line parallel to 3x -4y-10=0. The equation of this line is y= 3/4x - 1.75. The y-intercept is -1.75. Now we have two points on the opposite sides of the circle, (1, -1) and (0,-1.75). The midpoint formula will give you the centre of the circle and the distance formula will provide the radius.

Let me know if you have any questions.

Good luck.

Paul

Desmos Beautiful Free Math

I noticed that the two lines are perpendicular to each other and the point (1,-1) appears to be on the right side of the circle, on a line parallel to 3x -4y-10=0. The equation of this line is y= 3/4x - 1.75. The y-intercept is -1.75. Now we have two points on the opposite sides of the circle, (1, -1) and (0,-1.75). The midpoint formula will give you the centre of the circle and the distance formula will provide the radius.

Let me know if you have any questions.

Good luck.

Paul

Desmos Beautiful Free Math

Jun 09, 2014 | Office Equipment & Supplies

First of all you equation is not one : it has nothing on the right side of the = sign. But to answer the general question let us write the equation as **50+25x-5y=0**

**X-intercept (also know as roots) There may be several**

Definition: X-intercepts are those values of the independent variable x**for which y=0**. For a straight line there con be at most 1 x-intercept.

To find the intercept, set y=0 in the equation of the line and solve for x

50+25x-5(0)=0 or 50+25x=0. The solution is** x=-(50/25)=-2**

**Y-intercept (also know as the initial value.** There can only be 1 y-intercept, otherwise the expression does not represent a function.

Definition: It is the value of the dependent variable y when x=0 (where the function crosses the y-axis

To find it, set the x-value to 0 in the equation of the line.

**50+25x-5y=0**

50+25(0)-5y=0, or 50-5y=0. The solution is**y=50/5=10**

The straight line cuts the x-axis at the point (-2, 0) and the y-axis at the point (0,10)

Definition: X-intercepts are those values of the independent variable x

To find the intercept, set y=0 in the equation of the line and solve for x

50+25x-5(0)=0 or 50+25x=0. The solution is

Definition: It is the value of the dependent variable y when x=0 (where the function crosses the y-axis

To find it, set the x-value to 0 in the equation of the line.

50+25(0)-5y=0, or 50-5y=0. The solution is

The straight line cuts the x-axis at the point (-2, 0) and the y-axis at the point (0,10)

Jan 28, 2014 | Computers & Internet

By definition, the y-intercept is the value of y when x=0. Just set x=0 in the equation and solve for y.

Hence 3(0)+6y=90 or 6y=90. This gives y=90/6=15. The point of intercept of the y-axis is (0,15).

To get the x-intercept, set y= 0 in the equation and solve for x.

3x+6(0)=90 or 3x=90. This gives x=90/3=30.

The point of intercept of the x-axis is (30,0).

Hence 3(0)+6y=90 or 6y=90. This gives y=90/6=15. The point of intercept of the y-axis is (0,15).

To get the x-intercept, set y= 0 in the equation and solve for x.

3x+6(0)=90 or 3x=90. This gives x=90/3=30.

The point of intercept of the x-axis is (30,0).

Jan 20, 2012 | SoftMath Algebrator - Algebra Homework...

x-intercept (or zero of the function)

Set y=0 in the equation and solve fo x: 2x-5(0)=20 and x=20/2=10

y-intercept (initial value)

Set x= 0 in the equation and solve for y: 2(0)-5y=20 and y=20/(-5)=-4

If the equation is in the slope-intercept form y=ax+b

1. y-intercept is b

2. To get the x-intercept ( zero of the function) Set y=0=ax+b, and x=-b/a

Set y=0 in the equation and solve fo x: 2x-5(0)=20 and x=20/2=10

y-intercept (initial value)

Set x= 0 in the equation and solve for y: 2(0)-5y=20 and y=20/(-5)=-4

If the equation is in the slope-intercept form y=ax+b

1. y-intercept is b

2. To get the x-intercept ( zero of the function) Set y=0=ax+b, and x=-b/a

Aug 27, 2011 | Texas Instruments TI-84 Plus Calculator

This should start wit X=something and Y=something, sorry I'm not an human algebra calculator....

Jul 29, 2011 | Computers & Internet

use the slope-intercept form to graph y=2/3x+4

Mar 31, 2010 | Computers & Internet

assuming the question is what is the circle equation?

and if (-2,2) is the center of the circle

the equation should look like this: (x+2)^2+(Y-2)^2=R^2

And now only R is needed.

given 2x-5y+4=0 equation of line perpendicular

we can rearange the equation to be y=(2x+4)/5

from that we can see that the slope of the line is 2/5

And from the fact of perpendicular line we can say that the slope

of the radius line is -2/5.

The motivation now is to calculate the distance between the center of the circle to the cross point of the radius with the line perpendicular

For that we would calculate the radius line equation and compare it to the equation of line perpendicular

As mentioned earlier the slope of the radious line is -2/5.

So the equation is y=-2/5x+b and b can be calculated by using the center of the circle coordinates

2= - (2/5)*(-2)+b ------> b=2-4/5=1.2

radius equation is y=-(2/5)x+1.2

Now the cross point is calculated by comparing the equations:

-(2/5)x+1.2=(2x+4)/5 --> -2x+6=2x+4 --> 4x=2 --> x=1/2 --> y=1

So the cross point is (1/2,1).

The distance between the points is calculated by the following

Formula:

R=SQR(((1/2)-(-2))^2+(2-1)^2)=SQR(2.5^2+1^2)=SQR(6.25+1)=

SQR(7.25)

Therefore the circle eq is (x+2)^2+(Y-2)^2=7.25

and if (-2,2) is the center of the circle

the equation should look like this: (x+2)^2+(Y-2)^2=R^2

And now only R is needed.

given 2x-5y+4=0 equation of line perpendicular

we can rearange the equation to be y=(2x+4)/5

from that we can see that the slope of the line is 2/5

And from the fact of perpendicular line we can say that the slope

of the radius line is -2/5.

The motivation now is to calculate the distance between the center of the circle to the cross point of the radius with the line perpendicular

For that we would calculate the radius line equation and compare it to the equation of line perpendicular

As mentioned earlier the slope of the radious line is -2/5.

So the equation is y=-2/5x+b and b can be calculated by using the center of the circle coordinates

2= - (2/5)*(-2)+b ------> b=2-4/5=1.2

radius equation is y=-(2/5)x+1.2

Now the cross point is calculated by comparing the equations:

-(2/5)x+1.2=(2x+4)/5 --> -2x+6=2x+4 --> 4x=2 --> x=1/2 --> y=1

So the cross point is (1/2,1).

The distance between the points is calculated by the following

Formula:

R=SQR(((1/2)-(-2))^2+(2-1)^2)=SQR(2.5^2+1^2)=SQR(6.25+1)=

SQR(7.25)

Therefore the circle eq is (x+2)^2+(Y-2)^2=7.25

Oct 26, 2008 | Casio FX-115ES Scientific Calculator

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