Question

Find the equation of the hyperbola satisfying the given conditions:

Foci (±5, 0), the transverse axis is of length 8.

Answer 1

Foci (±5, 0), the transverse axis is of length 8.

Here, the foci are on the x-axis.

Therefore, the equation of the hyperbola is of the form ${\displaystyle \frac{x^2}{a^2}-\frac{y^2}{b^2}=1}$

Now, Foci are (±5, 0), c = 5.

Length of transverse axis 8, 2a = 8 = a = 4.

We know that a² + b² = c².

Therefore, 4² + b² = 5²

b² = 25 - 16 = 9

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