Question

Write the general equation for the circle that passes through the points (-5,0), (0.4), and (2,4).

You must include the appropriate sign for -) in your answer. Do not use spaces in your answer.

Answer 1

(x-1)^2+(y+19/8)^2=2665/64

Explanation:

The general equation of a circle is

(x - h)^2 + (y - k)^2 = r^2

Substituting the values of the 3 given points:

(-5 - h)^2 + (0 - k)^2 = r^2

(0 - h)^2 + (4 - k)^2 = r^2

(2 - h)^2 + (4 -k)^2 = r^2

Subtracting the second equation from the first:

(-5-h)^2 - h^2 + k^2 - (4 - k)^2 = 0

25 + 10h + h^2 - h^2 + k^2 - 16 + 8k - k^2 = 0

10h + 8k = -9 ------------ (A).

Subtract the third equation for the second:

h^2 - (2 - h)^2 + 0 = 0

h^2 - 4 + 4h - h^2 = 0

4h = 4

h = 1.

Substituting for h in equation A:

10 + 8k = -9

8k = -19

k = -19/8

So r^2 = (-5-1)^2 + (0 + 19/8)^2 =

36 + 361/ 64

= 2665/64