Q. 113.8( 12 Votes )

# In each of the, find the equations of the hyperbola satisfying the given conditions.

Foci (0, 13), the conjugate axis is of length 24.

Answer :

Foci (0, 13), the conjugate axis is of length 24.

Here, the foci are on y-axis.

Thus,

The equation of the hyperbola is of the form

Since, the foci are (0, 13), c= 13

Since, the length of the conjugate axis is 24,

2b = 24 ⇒ b = 12

We know that, a^{2} + b^{2} = c^{2}

a^{2} + 12^{2} = 13^{2}

⇒ a^{2} = 169 – 144 = 25

Hence, the equation of the hyperbola is

Rate this question :

Find the equation of the hyperbola, the length of whose latus rectum is 4 and the eccentricity is 3.

RS Aggarwal - MathematicsFind the equation of the hyperbola whose foci are and the eccentricity is .

RS Aggarwal - MathematicsFind the equation of the hyperbola having its foci at and passing through the point P(3, 4).

RS Aggarwal - MathematicsFind the equation of the hyperbola whose foci are (0, ±10) and the length of whose latus rectum is 9 units.

RS Aggarwal - Mathematics