Question

What is the standard form of the equation of a circle with endpoints of a diameter at the points (7,8) and (-5,6)?

Answer 1

`(x-1)^2+(y-7)^2=37`

Explanation:

The center of the circle is the midpoint of the diameter, i.e. `((7-5)/2, (8+6)/2) = (1,7)`

Again, the diameter is the distance between the points s`(7,8)` and `(-5,6)` :

`sqrt((7-(-5))^2+(8-6)^2) = sqrt(12^2+2^2)=2sqrt(37)`

so the radius is `sqrt(37)`.

Thus the standard form of the circles equation is

`(x-1)^2+(y-7)^2=37`