Question

Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credit.

x2 − 4x + y2 + 8y = −4

Answer 1

Yes, but I don't know how to do that.

Answer 2

do you know how to complete the square....?

Answer 3

The general equation of a circle is:\[x^2+y^2+2gx+2fy+c=0\]

Answer 4

where the center is:\[(-g,-f)\]

Answer 5

so if you subtract 4 from both sides of the equation you get:\[x^2+y^2-4x+8y+4=0\]

Answer 6

in your case 2g is -4 and 2f is 8
so the center is (-g,-f) which is (2,-4)

Answer 7

so the center is (2,-4)

Answer 8

now the radius is given by:\[\sqrt{g^2+f^2-c}\]

Answer 9

ok @Hero

Answer 10

ok so in your case g is -2 and f is 4 and c is 4.
so the radius is:\[\sqrt{(-2)^2+4^2-4}\]
that simplifies to 4

so the radius of the circle is 4

Answer 11

there is also another equation of a circle which is:\[(x-h)^2+(y-k)^2=r^2\]
where the radius is r and the center is (h,k) but in your problem it was in general form so I used the other circle equation