Question about Casio FX-115ES Scientific Calculator

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

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 | Calculators

solution is:

x-5y = 20

-5y = 20-x

5y = x-20

y = (x-20) / 5

x-5y = 20

-5y = 20-x

5y = x-20

y = (x-20) / 5

Dec 14, 2015 | Calculators

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 | Calculators

There are an infinite number of solutions. The equation is that of a straight line, which has an infinite number of points. At any point on the line there is a unique value of y.

Nov 06, 2014 | Calculators

There are an infinite number of solutions. The equation is that of a straight line, which has an infinite number of points. At any point on the line there is a unique value of x.

Nov 06, 2014 | Calculators

3x-7y=2 is an equation of a line. That line doesn't go through the point (6, -7) though. Are you looking for the equation of a line through the point parallel to the first line? Perpendicular?

Jun 02, 2013 | Texas Instruments TI-84 Plus Calculator

Two lines are perpendicular if they belong to the same plane and intersect (cut) one another at right angle. They make a 90 degree angle. If you are doing analytic geometry, two lines are perpendicular if the product of their slopes ia equal to -1.

Other relative positions of lines are parallel (they have the same slope/direction) or they are just secant at an angle not equal to 90 degrees.

Other relative positions of lines are parallel (they have the same slope/direction) or they are just secant at an angle not equal to 90 degrees.

Feb 03, 2012 | Calculators

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

Hello,

And they are perpendicular. But due to the finite resolution of the screen they do not appear to be. However if you had a geometry application linked with the function graphing the measurement of the angle between the lines will show that it is 90 degrees, or 1.58 rad.

This screen capture from the TI'Nspire will convince you, I hope.

Hope it helps.

And they are perpendicular. But due to the finite resolution of the screen they do not appear to be. However if you had a geometry application linked with the function graphing the measurement of the angle between the lines will show that it is 90 degrees, or 1.58 rad.

This screen capture from the TI'Nspire will convince you, I hope.

Hope it helps.

Nov 04, 2009 | Texas Instruments TI-84 Plus Silver...

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