Question

16x^2+16y^2+64x-32y+55=0
Identify the conic and find the center, radius(for circle), and a and b(for ellipse or hyperbola) sketch the graph

Answer 1

first group and partially factor

16(x^2 + 4x + .....) + 16(y^2 - 2y + .....) = -55
complete the squares
16(x^2 + 4x + 4) + 16(y^2 - 2y + 1) = -55 + 64 + 16
16(x+2)^2 + 16(y - 1)^2 = 25
(x + 2)^2 + (y - 1)^2 = 25/16

identify the conic and state its properties