Question

Find the equation of the hyperbola satisfying the give conditions: Vertices (0, ±5), foci (0, ±8)

Answer 1

Vertices (0, ±5), foci (0, ±8)
Here, the vertices are on the y-axis.

Therefore, the equation of the hyperbola is of the form $\frac{x^2}{a^2} -\frac{ y^2}{b^2} = 1.$
Since the vertices are (0, ±5), a = 5.
Since the foci are (0, ±8), c = 8.

We know that $a ^2 + b ^2 = c^ 2 .$

$∴ 5^2 \+ b^2 = 8^2$
b2 = 64 – 25 = 39

∴ The equation of the hyperbola is $\frac{y^2}{25} – \frac{x^2}{39} = 1$