Question

Q: Convert 4x^2 + 4y^2 -8x -16y -29 = 0 into standard form.

I first started by pairing the like terms together, getting:
4x^2 -8x + 4y^2 -16y = 29

The next step, I'm a little confused. I know I need to complete the square, but I'm not sure how to fully factor out the above equation before doing so. Can someone help me getting the factored form of the above equation?

Thanks!

Answer 1

4x^2 -8x + 4y^2 -16y = 29
4(x^2 - 2x + ...) + 4(y^2 - 4y + ... ) = 29
4(x^2 - 2x + 1) + 4(y^2 - 4y + 4) = 29 + 4 + 16
4(x-1)^2 + 4(y-2)^2 = 49
divide by 4
(x-1)^2 + (y-2)^2 = 49/4

looks like a circle with centre at (1,2) and radius 7/2