Question

If a circle has a diameter with endpoints of (-3, 0) and (5, 4) then the equation of the circle is?

Answer 1

(x - 1)² + (y - 2)² = 20

Explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given the endpoints, then the centre is at the midpoint

C = [
`(-3+5)/(2)`,
`(0+4)/(2)` ] = (1, 2 )

The radius is the distance from the centre to either of the 2 endpoints.

Use the distance formula to find r

r =
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2 }`

with (x₁, y₁ ) = (1, 2) and (x₂, y₂ )= (- 3, 0)

r =
`√((-3-1)^2+(0-2)^2)`

=
`√((-4)^2+(-2)^2)`

=
`√(16+4)`

=
`√(20)`

Thus equation of circle is

(x - 1)² + (y - 2)² = (
`√(20)` )² , that is

(x - 1)² + (y - 2)² = 20