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Tangents are drawn from a point P to the...

Tangents are drawn from a point P to the hyperbola `x^2-y^2= a^2` If the chord of contact of these normal to the curve, prove that the locus of P is `1/x^2 - 1/y^2 = 4/a^2`

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Let locus of point `P(h,k)` `Eqn.` of tangent from point `P` to the hyperbola is: `y = mx pm sqrt(a^2*m^2 - a^2)` `y = mx pm a*sqrt(m^2 -1)` `Eqn.` of normal to this hyperbola: `a^2*y_1(x-x_1) + a^2*x_1(y-y_1)` Tangents starts from point `P(h,k)` , so it is point of contact. And since this point is normal to the curve, it satisfies `Eqn.` of normal. `a^2*k(x-h) + a^2*h(y-k) = 0` ...
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