Given: Axis of the hyperbola are equal, i.e. a = b

To prove: SP.S’P = CP²

Formula used:

The standard form of the equation of the hyperbola is,

Foci of the hyperbola are given by (±ae, 0)

Let P (m, n) be any point on the hyperbola

The distance between two points (m, n) and (a, b) is given by

C is Centre with coordinates (0, 0)

Now,

{∵ a² = m² – n²}

From (i):

Taking square root both sides:

Hence Proved