Question

The edges of the diameter of a circle are at (-3,-8) and (5,7).

Write the equation of the circle in general form.

Answer 1

`(x-8)^(2) +(y-15)^(2) =17^(2)`

Explanation:

subtract the xs and the ys to find the number in the parenthesees

-3 - 5 = -8

-8 - 7 = -15

so the equation is

`x^(2) +y^(2) =r^(2) \\(x-8)^(2) +(y-15)^(2) =r^(2)`

r is easy, count how far it is from one point to the next one or use the distance formula

`\sqrt{x^(2) +y^(2) } \\\sqrt{(-8)^(2) +(-15)^(2) } \\√(64 +225) \\√(289) \\17`

so the final equation is

`(x-8)^(2) +(y-15)^(2) =17^(2)`