Question

The length of the transverse axis along x-axis with centre at origin of a hyperbola is 7 and it passes through the point (5, –2). The equation of the hyperbola is ______.

Options

• `4/49 x^2 - 196/51 y^2` = 1

• `49/4 x^2 - 51/196 y^2` = 1

• `4/49 x^2 - 51/196 y^2` = 1

• None of these

Answer 1

The length of the transverse axis along x-axis with centre at origin of a hyperbola is 7 and it passes through the point (5, –2). The equation of the hyperbola is `4/49 x^2 - 51/196 y^2` = 1.

Explanation:

Let `x^2/a^2 - y^2/b^2` = 1 represent the hyperbola.

Then according to the given condition

The length of the transverse axis

i.e., 2a = 7

⇒ a = `7/2`.Also, the point (5, –2) lies on the hyperbola

So, we have `4/49 (25) - 4/b^2` = 1

Which gives `b^2 = 196/51`.

Hence, the equation of the hyperbola is `4/49 x^2 - 51/196 y^2` = 1.