If the ordinate MP of a hyperbola be produced to Q, so that MQ is equal to either of the focal distances of P, prove that the locus of Q is a pair of parallel straight lines.

A point P moves such that the sum of the slopes of the normals drawn from it to the hyperbola xy=4 is equal to the sum of the ordinates of feet of normals. The locus of P is a curve C. Q.If the tangent to the curve C cuts the coordinate axes at A and B, then , the locus of the middle point of AB is

In a rectangular hyperbola, prove that the product of the focal distances of a point on it is equal to the square of its distance from the centre of the hyperbola .

PQ is a double ordinate of the parabola y^2 = 4ax. If the normal at P intersect the line passing through Q and parallel to axis of x at G, then locus of G is a parabola with -

If normal at P to a hyperbola of eccentricity 2 intersects its transverse and conjugate axes at Q and R, respectively, then prove that the locus of midpoint of QR is a hyperbola. Find the eccentricity of this hyperbola

The ordinate of any point P on the hyperbola, given by 25x^(2)-16y^(2)=400 ,is produced to cut its asymptotes in the points Q and R. Prove that QP.PR=25.

Let any double ordinate PNP^(1) of the hyperbol (x^(2))/(9)-(y^(2))/(4)=1 be produced both sides to meet the asymptotes in Q and Q', then PQ.P'Q is equal to