Question 43399
{{{4y^2 - x^2 + 8y + 4x - 4 = 0}}}
{{{4y^2 + 8y - x^2 + 4x = 4}}}
{{{(4y^2 + 8y) - (x^2 + 4x) = 4}}}
{{{4(y + 1)^2 - (x + 2)^2 = 4 + 4 + 4}}}
{{{((y + 1)^2)/2 - ((x + 2)^2)/8 = 1}}}
Vertex: (-2,-1)
Transverse Axis: vertical (opens up and down)
A = {{{sqrt(2)}}}
B = {{{sqrt(8)}}}
Asymptotes:
Slope(M) = +-A/B = +-{{{sqrt(2)/sqrt(8)}}} = +-{{{sqrt(2)/(2*sqrt(2))}}} = +-{{{1/2}}}
{{{y - y1 = M(x - x1)}}}
{{{y + 1 = 0.5(x + 2)}}} and {{{y + 1 = -0.5(x + 2)}}}
{{{y + 1 = 0.5x + 1}}} and {{{y + 1 = -0.5x - 1}}}
{{{y = 0.5x}}} and {{{y = -0.5x - 2}}}
{{{ graph( 1200, 600, -20, 20, -10, 10, -1+sqrt(2 + 2((x+2)^2)/8), -1-sqrt(2 + 2((x+2)^2)/8), 0.5x, -0.5x - 2 ) }}}