Q. 103.7( 3 Votes )

# If P is any point on the hyperbola whose axis are equal, prove that SP.S’P = CP^{2}

Answer :

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

**To prove:** SP.S’P = CP^{2}

**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,

{∵ a^{2} = m^{2} – n^{2}}

From (i):

Taking square root both sides:

**Hence Proved**

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