Question

Find the equation of hyperbola whose foci are (±√29, 0) and the transverse axis is of the length 10.

Answer 1

Major axis of the given hyperbola lie on x-axis.

Equation of the hyperbola will be of the form: x²/a² – y²/b² = 1

Whose foci at (±c, 0) and transverse axis is 2a

Given: transverse axis = 10

⇒ 2a = 10 ⇒ a = 5

Given: foci (±√29, 0)

(±c, 0) = (±√29, 0)

⇒ c = √29

We know, c² = a² + b²

29 = 25 + b²

or b² = 4

Equation (1)⇒

x²/25 – y²/4 = 1

Which is required equation.