Question

Find the equation of the hyperbola satisfying the give 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 $\frac{x^2}{a^2} –\frac{ y^2}{b^2} = 1.$
Since the foci are (±5, 0), c = 5.

Since the length of the transverse axis is 8,
2a = 8
$⇒$ a = 4.
We know that
a2 + b2 = c2 .
∴ 42 + b2 = 52
$⇒$ b2 = 25 – 16= 9

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