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

A point P moves such that sum of the slopes of the normals drawn from it to the hyperbola xy=16 is equal to the sum of ordinates of feet of normals. The locus of P is a curve C

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

If tangents P Qa n dP R are drawn from a variable point P to thehyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,(a > b), so that the fourth vertex S of parallelogram P Q S R lies on the circumcircle of triangle P Q R , then the locus of P is (a) x^2+y^2=b^2 (b) x^2+y^2=a^2 (c) x^2+y^2=a^2-b^2 (d) none of these

Find the equation of the normal to the hyperbola x^(2)-y^(2)=9 at the point p(5,4).

If the chord of contact of tangents from a point P to the parabola y^2=4a x touches the parabola x^2=4b y , then the locus of Pdot is a) a cicle b) a parabola c) a straight line d) none of these

If the normal at a point P to the hyperbola x^2/a^2 - y^2/b^2 =1 meets the x-axis at G , show that the SG = eSP.S being the focus of the hyperbola.

The locus of the center of the circle touching the line 2x-y=1 at (1,1) is (a) x+3y=2 (b) x+2y=2 (c) x+y=2 (d) none of these

A point P moves such that the sum of the slopes of the normals drawn from it to the hyperbola xy = 16 is equal to the sum of ordinates of feet of normals . The locus of P is a curve C. the equation of the curve C is

Let P be a point on the hyperbola x^2-y^2=a^2, where a is a parameter, such that P is nearest to the line y=2xdot Find the locus of Pdot