I need to find the center and radius of the circle with this equation: x^2 + y^2 + 6x - 8y - 25 = 0?

Question

if anyone has an answer it would really be appriciated

Answer 1

what grade are you going to?

Answer 2

First we need to get it in the form

(x - xo)^2 + (y - yo)^2 = r^2

where {xo,yo} is the center of the circle and r is the radius

so

x^2 + 6x + 9= (x + 3)^2

we don't see that 9 in the equation so we'll just add it to both sides

x^2 + y^2 + 6x - 8y - 25 + 9= 0 + 9

Now we do the same thing for y

y^2 - 8y + 16 = (y - 4)^2

Again, we don't see the 16 there so we add it to both sides

x^2 + y^2 + 6x - 8y - 25 + 9 + 16 = 0 + 9 +16

OR

(x^2 + 6x + 9) + (y^2 - 8y + 16) - 25 = 25

OR

(x +3)^2 + (y -4)^2 = 50

So we have a circle of radius Sqrt[50] = 5 Sqrt[2] centered at {-3,4}