Question

Classify the conic and write the equation in standard form:

(1) 9x^2 + 9y^2 + 18x - 18y = 0

(2) 16x^2 + 16y^2 - 64x + 32y + 55 = 0

(3) 6x^2 + 2y^2 + 18x - 10y + 2 = 0

Answer 1

the first two are circles, the last one is an ellipse

I will do the second one by
completing the square,

16x^2 + 16y^2 - 64x + 32y + 55 = 0
16(x^2 - 4x+ ___) + 16(y^2 + 2y + ___) = -55
16(x^2 - 4x+ 4) + 16(y^2 + 2y + 1) = -55+64+16
16(x^2 - 4x+ 4) + 16(y^2 + 2y + 1) = 25
(x-2)^2 + (y+1)^2 = 25/16

Answer 2

Oh, I see what I was doing wrong. I thought you had to SUBTRACT the numbers from the other side when you complete the square, but you have to ADD them. I get it now. Thanks!