Question

Find the equation of a circle with the points (-3,8) and (7,6) at the end points of a diameter

Answer 1

(x - 2)² + (y - 7)² = 26

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 coordinates of the centre are at the midpoint of the endpoints of the diameter and the radius is the distance from the centre to either of the 2 endpoints

Find the centre using the midpoint formula

centre = [
`(1)/(2)`(- 3 + 7),
`(1)/(2)`(8 + 6)] = (2, 7)

to find the radius use the distance formula

r = √(x₂ - x₁)² + (y₂ - y₁)²

with (x₁, y₁ ) = 2, 7) and (x₂, y₂ ) = (7, 6)

r =
`√((7-2)^2+(6-7)^2)` =
`√(25+1)` =
`√(26)`

centre (2, 7 ) and r² = (
`√(26)`)² = 26, hence

(x - 2)² + (y - 7)² = 26 ← equation of circle