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# Analytic geometry (-2,2) 2x-5y+4=0 equation of line perpendicular

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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

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Posted on Jan 02, 2017

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### The equation of the straight line PQ is 3-2kx+k+1=12,calculate,in each case,the numerical value of k if the line PQ is parrallel to the line y=4x+7;is perpendicular to the line y=4x+7;

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.

Apr 12, 2017 | Homework

1 Answer

### Write an equation in slope intercept form that passes through (-4,7) and is perpendicular to y+4=1/4(x-7)

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

Apr 03, 2016 | Office Equipment & Supplies

1 Answer

### 8x + 3y = 3 4x + 5y = -23

This is best written as two separate equations:

8x+3y = -23 and 34x+ 5y = -23
Solving the first one for x:
8x = -23-3y
x = -23/8 - 3/8y
Substituting this value for x into the second equation:
34(-23/8 - 3/8y) + 5y = -23
-97.75 - (34)(.375)y + 5y = -23
-97.75 - 12.75y + 5y = -23
-97.75 -7.75y = -23
-7.75y = 97.75-23=74.75
y = -74.75/7.75 = -9.645161
Substitution back into the equation for x:
x = -23/8 - 3/8(-9.645161)
x = -2.875 + 3.616935
x =.741935

Dec 12, 2014 | Bagatrix Algebra Solved! 2005 (105101) for...

1 Answer

### X and y intercepts

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)

Jan 28, 2014 | Computers & Internet

1 Answer

### What are perpendicular lines

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.

Feb 03, 2012 | Office Equipment & Supplies

1 Answer

### Write an equation of the line in standard form that pass through (-5,-11) and 10,7)

Calcualte the slope of the line as
a=(7-(-11))/(10-(-5))=18/15=6/5
Use the fact that the line passes through one of the two points, for example (10,7)
7=(6/5)*10+b=12+b
Obtain b as b=7-12=-5
The equation of the line in functional form is y=(6/5)x-5
Multiply everything by 5 to clear the fraction
5y=6x-25 or 0=6x-5y-25
Finally, the equation in general form (standard?) is 6x-5y-25=0.

Check the calculation by verifying that the point (10,7) lies on the line.
6(10)-5(7)-25=60-35-25=60-60=0 CHECKed!
Check that the second point (-5,-11) lies on the line also (if you want to)
6*(-5)-5*(-11)-25=-30+55-25=0
That checks OK.

Dec 04, 2011 | Super Tutor Pre Algebra (ESDPALG)

1 Answer

### How do I use this calculator to find the x and y intercepts when the problem has both the x and y letters. it will not allow me to enter the full equation. example problem is 2x-5y=20 and I need to find...

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

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

1 Answer

### I own a ti-84 plus silver edition, and when i enter two equations y=2x+3 and y=(-.5x)+3 They should be perpendicular lines.

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.

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

1 Answer

### Analytic geometry

nice..let's see..counts on fingers..

x=a(b)-(d-n)/z.com

Feb 18, 2008 | Dell GX270 P4 256/40/48X/XPP/NONE...

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