Question

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

x^2 − 4x + y^2 + 8y = −4

Answer 1

first you need to convert this equation to (x-h)^2+(y-k)^2=r^2 where r is radius

Answer 2

I know that 4 is the radius but I just cant find the rest of it.

Answer 3

x^2 − 4x + y^2 + 8y = −4
(x^2-4x) + (y^2-6y)=-4
(x^2-4x+4)+(y^2-6y+9)=-4+4+9
(x-2)^2+(y-3)^2=9

Answer 4

thus the radius is sqrt9=3, and the center is (2, 3)

Answer 5

(x-h)^2+(y-k)^2=r^2 where r is radius and (h, k) is center

Answer 6

Oh.. Thank you for explaining it to me and working it out :).

Answer 7

wait i made amistake

Answer 8

wait

Answer 9

Oh. okay!

Answer 10

it should be:
x^2 − 4x + y^2 + 8y = −4
(x^2-4x)+(y^2+8y)=-4
(x^2-4x+4)+(y^2+8y+16)=-4+16+4
(x-2)^2+(y+4)^2=16
thus the center is (2, -4) and radius is sqrt16=4

Answer 11

Thank you! :)