Question

The points (0, -8) and (10, 2) represent the endpoints of a diameter of a circle. Which of the following represents the equation of this circle?

Answer 1

(x-5)²+(y+2)²=200.

Explanation:

1) using the given coordinates it is possible to calculate

- the centre of the given circle:

`x_0=(10+0)/(2)=5; \ y_0=(2-8)/(2)=-2;`

- the radius of the given circle:

`r=√((10-0)^2+(2+8)^2) =√(200) ;`

2) finally, the required equation (common form is (x-x₀)²+(y-y₀)²=r²):

(x-5)²+(y+2)²=200.