How do you find an equation of hyperbola with given endpoints of the transverse axis: (0,-6),(0,6); Asymptote: y=3/10 x?

Feb 8, 2016

${y}^{2} / 36 - {x}^{2} / 400 = 1$

Explanation:

Equation of parabola and asymptote
1) ${y}^{2} / {a}^{2} - {x}^{2} / {b}^{2} = 1$
2) $y = \pm \frac{a}{b} x$
3) a = 6; y = 3/10x; 3/10 = 6/b; b = 20
Now substitute:
${y}^{2} / 36 - {x}^{2} / 400 = 1$