What is the locus of P if it`s polar with respect to the hyperbola (x^2/a^2-y^2/a^2)=1 be equally inclined to the coordinate axes?

Question

Deepak Kumar Shringi · Answer

equation of a polar is always T=0 with respect to the pole here polar is equally inclined to axes that means slope is -1,1
now T=0
xx₁/a² – yy₁/b²=1
slope is x₁b²/y₁a²=1 or -1
then x₁/y₁= a²/b²

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What is the locus of P if it`s polar with respect to the hyperbola (x^2/a^2-y^2/a^2)=1 be equally inclined to the coordinate axes?

What is the locus of P if it`s polar with respect to the hyperbola (x^2/a^2-y^2/a^2)=1 be equally inclined to the coordinate axes?

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