Question

Find the center and vertices of the ellipse.
x2 + 4y2 - 4x + 8y + 4 = 0

Answer 1

x^2 +4y^2-4x+8y+4=0 to clarify

Answer 2

Complete the squares
\[x ^{2}-4x+4+4y ^{2}+8y+4=4\]
\[(x-2)^{2}+(2y+2)^{2}=2^{2}\]
so the center is (2,-1)

If x=2, y=-2 or y=0
If y=-1, x=4 or x=0
(2,-2),(2,0),(4,-1),(0.-1)

Answer 3

thank you!! :)