Find the equation of the hyperbola having its foci at and passing through the point P(3, 4).

Given: Foci at and passing through the point P(3, 4)

Need to find: The equation of the hyperbola.

Let, the equation of the hyperbola be:

It passes through the point P(3, 4)

So putting the values of (x, y) we get,

⇒ ---- (1)

Foci at

So,

We know,

⇒

⇒

⇒ [Squaring on both sides]

⇒ ---- (2)

Comparing (1) and (2) we get,

Solving the equations we get,

b₁ =

b₂ =

b₃ =

b₄ =

With the help of any of these values of b we can’t find out the equation of the hyperbola.

* This is the only process we can apply in this standard.