If `P N` is the perpendicular from a point on a rectangular hyperbola `x y=c^2` to its asymptotes, then find the locus of the midpoint of `P N`

Find the product of the length of perpendiculars drawn from any point on the hyperbola x^2-2y^2-2=0 to its asymptotes.

The tangent at any point P on the circle x^2+y^2=4 meets the coordinate axes at Aa n dB . Then find the locus of the midpoint of A Bdot

P Q and R S are two perpendicular chords of the rectangular hyperbola x y=c^2dot If C is the center of the rectangular hyperbola, then find the value of product of the slopes of C P ,C Q ,C R , and C Sdot

If the sum of the slopes of the normal from a point P to the hyperbola x y=c^2 is equal to lambda(lambda in R^+) , then the locus of point P is (a) x^2=lambdac^2 (b) y^2=lambdac^2 (c) x y=lambdac^2 (d) none of these

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.

If the tangents to the parabola y^2=4a x intersect the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at Aa n dB , then find the locus of the point of intersection of the tangents at Aa n dBdot

If the two tangents drawn from a point P to the parabola y^(2) = 4x are at right angles then the locus of P is

The tangent at P on the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2))=1 meets one of the asymptote in Q. Then the locus of the mid-point of PQ is

A point P moves such that the chord of contact of the pair of tangents from P on the parabola y^2=4a x touches the rectangular hyperbola x^2-y^2=c^2dot Show that the locus of P is the ellipse (x^2)/(c^2)+(y^2)/((2a)^2)=1.