Q. 103.7( 3 Votes )

If P is any point on the hyperbola whose axis are equal, prove that SP.S’P = CP2

Answer :

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)


{ a2 = m2 – n2}

From (i):

Taking square root both sides:

Hence Proved

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses