Question

Find the equation of the hyperbola satisfying the give conditions: Vertices (±2, 0), foci (±3, 0)

Answer 1

Vertices (±2, 0), foci (±3, 0)
Here, the vertices are on the x-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 (±2, 0), a = 2.
Since the foci are (±3, 0), c = 3.

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

$∴ 2^2 \+ b^2 = 3^2$
$b^2 = 9 – 4 = 5$

∴ The equation of the hyperbola is $\frac{x^2}{4} –\frac{ y^2}{5} = 1$