Question

Find an equation of the circle whose diameter has endpoints (2,3) and (-4,5)

Answer 1

(x+1)² + (y-4)² = 10

Explanation:

The diameter of a circle has the endpoints at (2,3) and (-4,5).

Therefore, the length of the diameter is given by

`\sqrt{(2-(-4))^(2)+(3-5)^(2)}` = 2
`√(10)`

Hence, the radius of the circle is √10.

Now the midpoint of the line joining (2,3) and (-4,5) will be the center of the straight line.

Hence, the center will be at (
`(2-4)/(2),(3+5)/(2)) =(-1, 4)`

Therefore the equation of the circle is

(x+1)² + (y-4)² = (√10)²

⇒ (x+1)² + (y-4)² = 10 (Answer)