Question

Find the equation of the hyperbola satisfying the give conditions: Vertices (0, ±3), foci (0, ±5)

Answer 1

Vertices (0, ±3), foci (0, ±5)
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, ±3), a = 3.
Since the foci are (0, ±5), c = 5.

We know that $a^2 \+ b^2 = c^2 .$
$∴ 3^2 \+ b^2 = 5^2$
$⇒ b^2 = 25 – 9 = 16$

Thus, the equation of the hyperbola is$\frac{y^2}{9} – \frac{x^2}{16} = 1$