Question 43057
{{{y^2 = 5x^2 + 25}}}
{{{y^2 - 5x^2 = 25}}}
{{{(y^2/25) - (5x^2/25) = 25/25}}}
{{{(y^2/25) - (x^2/5) = 1}}}
This is a hyperbola.
Transverse axis: vertical
Center: (0,0)
a = 5
b = {{{sqrt(5)}}}
Vertex:(0,5) and (0,-5)
{{{a^2 + b^2 = c^2}}}
{{{5^2 + (sqrt(5))^2 = c^2}}}
{{{25 + 5 = c^2}}}
{{{sqrt(30) = c}}}
Foci: (0,{{{sqrt(30)}}}) and (0,{{{-sqrt(30)}}})
Asymptote:
slope: (+-a/b) = +-{{{5/sqrt(5)}}} = +-{{{(5*sqrt(5))/(sqrt(5)*sqrt(5))}}} = +-{{{sqrt(5)}}}
center (again): (0,0)
{{{y - y1 = m(x - x1)}}}
{{{y - 0 = sqrt(5)(x - 0)}}} and {{{y - 0 = -sqrt(5)(x - 0)}}}
{{{y = sqrt(5)x}}} and {{{y = -sqrt(5)x}}}
{{{ graph( 600, 600, -10, 10, -10, 10, sqrt(5x^2 + 25), -sqrt(5x^2 + 25), sqrt(5)x, -sqrt(5)x ) }}}