Question

If P = (-4,-3) and Q = (2, 1) are the

endpoints of the diameter of a circle,
find the equation of the circle.
(x - [?])2 + (y - [ ])2 = [
]​

Answer 1

(x - 1)2 + (y - 1)2 = 13

Explanation:

This is the answer for Acellus users

Answer 2

`(x+1)^2 + (y + 1)^2 = 13`

Explanation:

To find the centre of the circle, find the mid - point of PQ :

`Centre =( (x_1+x_2)/(2) \ , \ (y_1 + y_2)/(2)) = ((-2)/(2) \ , \ (-2)/(2)) = (-1, -1)`

Diameter = 2 x Radius , To Find the diameter, find distance between P and Q:

`Distance , PQ = √((2 - (-4))^2 + (1 -(-3))^2)`

`= √(6^2 + 4^2) = √(36+ 16) = √(52) = √(4 * 13) = 2 * √(13)`

PQ is the diameter , therefore radius :

`r = (1)/(2) * 2 √(13) = √(13)`

Equation of a circle :

`(x + 1)^2 + (y + 1)^2 = 13`