Question

Does anyone know how to solve this??

Answer 1

(x - 3)² + (y + 1)² = 65

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

The centre C is at the midpoint of the endpoints of the diameter.

Using the midpoint formula to find C

C = (
`(7-1)/(2)`,
`(6-8)/(2)` ) = (
`(6)/(2)`,
`(-2)/(2)` ) = (3, - 1 )

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

Using the distance formula to find r

with C (3, - 1 ) and (7, 6 ) , then

r =
`√((7-3)^2+(6+1)^2)`

=
`√(4^2+7^2)`

=
`√(16+49)`

=
`√(65)`

Then equation of circle is

(x - 3)² + (y - (- 1) )² = (
`√(65)` )², that is

(x - 3)² + (y + 1)² = 65 ← equation of circle