hyperbolas 6

Question

Find an equation in standard form for the hyperbola with vertices at (0, ±10) and asymptotes at 
y = ±

Answer 1

The vertices of hyperbola is (0, 10) and (0, -10) and asymptote y = ± (5/4)x.

The standard form of equation of hyperbola with center at the origin (where a and b are not equals to 0) is

x ²/a ² - y ²/b ² = 1 (Transverse axis is horizontal) or y ²/a ²- x ²/b ² = 1 (Transverse axis is vertical).

The y - coordinates of the  vertices points are 10 and - 10.

The value of a = 10, because the vertices are 10 units from the center.

Because the transverse axis is vertical, the asymptotes are of the forms y = (a/b) x and y = - (a/b) x.

The asymptote y = ± (5/4)x is comparison with y = ± (a/b) x.

a/b= 5/4 ------> 10/b = 5/4 ------>b = 8 and a = 10.

The standard form of the hyperbola equation is y²/10 ² - x ²/8 ² = 1.