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)





Now,







{ a2 = m2 – n2}





From (i):



Taking square root both sides:




Hence Proved


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