Question

Write the general equation for the circle that passes through the points:

(-1, 2)
(4, 2)
(- 3, 4)

Answer 1

Explanation:

let the eq. of circle be x²+y²+2gx+2fy+c=0 ...(1)

∵ it passes through (-1,2),(4,2),(-3,4)

∴ (-1)²+2²-2g+4f+c=0

-2g+4f+c=-5 ...(2)

4²+2²+8g+4f+c=0

8g+4f+c=-20 ...(3)

(-3)²+4²-6g+8f+c=0

-6g+8f+c=-25 ...(4)

(3)-(2) gives

10 g=15

2g=3

g=3/2

(3)-(4) gives

14 g-4f=5

14×(3/2)-4f=5

-4f=5-21=-16

f=4

from (2)

-2(3/2)+4×4+c=-5

-3+16+c=-5

c=-5-13

c=-18

so eq. of circle is

x²+y²+2(3/2)x+2(4)y-18=0

x²+y²+3x+8y-18=0