SOLUTION: How do i Write the equation of a circle with endpoints of the diameter at (4, -3) and (-2, 5).

Question 551180: How do i Write the equation of a circle with endpoints of the diameter at
(4, -3) and (-2, 5).

Found 2 solutions by jim_thompson5910, nyc_function:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Recall that the general equation of a circle is .

So we need the center (h,k) and the radius squared .

First, let's find the center (h,k).

Since the center is the midpoint of the line segment with endpoints (4,-3) and (-2,5), we need to find the midpoint.

X-Coordinate of Midpoint =

Since the x coordinate of midpoint is , this means that

Y-Coordinate of Midpoint =

Since the y coordinate of midpoint is , this means that

So the center is the point (1, 1)

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Now let's find the radius squared

Use the formula , where (h,k) is the center and (x,y) is an arbitrary point on the circle.

In this case, and . Also, and . Plug these values into the equation above and simplify to get:

So because , , and , this means that the equation of the circle that passes through the points (4,-3) and (-2,5) (which are the endpoints of the diameter) is

.

Answer by nyc_function(2741) (Show Source): You can put this solution on YOUR website!
Use the Midpoint Formula to find the circle's center. The Midpoint Formula is ((x1+x2)/2, (y1+y2)/2) or (average of the x-coordinates, average of the y-coordinates). The average of the x-coordinates is h, and the average of the y-coordinates is k.

h = (-2 + 4)/2

h = 2/2

h = 1

k = (-3 + 5)/2

k = 2/2

k = 1
This circle is centered at the point (1,1).
We now find the distance from one of the given points and the center point (1,1).

The radius is 5.

We now plug into the general equation of the circle formula.

(x - 1)^2 + (y - 1)^2 = (5)^2

(x - 1)^2 + (y - 1)^2 = 25
If you don't understand, write back....

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