Mathematics | MHT CET 2019 | Discussion Page

If $P( x_{1},y_{1})$ is a point on the hyperbola x²-y² =a² , then SP.S'P=.....

$\frac{x_{1}^{2}-y_{1}^{2}}{a^{2}}$

$\frac{x_{1}^{2}+y_{1}^{2}}{a^{2}}$

$x_{1}^{2}-y_{1}^{2}$

$x_{1}^{2}+y_{1}^{2}$

Option D

Given , equation of hyperbola

x²-y² =a²..............(i)

If P(x₁,y₁) is a point on Eq.(i) , then

$x_{1}^{2}-y_{1}^{2}$ = $a_{}^{2}$ ......(ii)

Now, SP= ex₁-a

and SP'= ex₁+a

$\therefore$ SP.SP' = (ex₁-a)(ex₁+a)

= e².x₁²-a²

= $2x_1^2-a^{2}$ (since , for x²-y²= a², e = $\sqrt{2}$ )

= $2x_1^2-(x_1^2-y_1^2)$ [using Eq. (ii)]

= $x_1^2+y_1^2$

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