Tangents are drawn from a point P to the hyperbola `x^2/2-y^2= 1` If the chord of contact is a normal chord, then locus of P is the curve`8/x^2 - 1/y^2 = lambda` where `lambda in N` .Find `lambda`

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))

Tangents are drawn from the point (-1,2) to the parabola y^(2)=4x The area of the triangle for tangents and their chord of contact is

Tangents are drawn from any point on the hyperbola (x^(2))/(9)-(y^(2))/(4)=1 to the circle x^(2)+y^(2)=9. Find the locus of the midpoint of the chord of contact.

From a point P tangents are drawn to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 If the chord of contact touches the auxiliary circle then the locus of P is

The locus of the point x=a+lambda^(2),y=b-lambda where lambda is a parameter is

From a point on the line x-y+2-0 tangents are drawn to the hyperbola (x^(2))/(6)-(y^(2))/(2)=1 such that the chord of contact passes through a fixed point (lambda, mu) . Then, mu-lambda is equal to

From a point P, tangents are drawn to the hyperbola 2xy = a^(2) . If the chord of contact of these tangents touches the rectangular hyperbola x^(2) - y^(2) = a^(2) , prove that the locus of P is the conjugate hyperbola of the second hyperbola.