Let P be a point such that the sum of the slopes of normals drawn from the point P to the rectangular hyperbola`xy=16`is equal to the sum of ordinates of the feet of normals.Prove that the locus of P is a parabola.find its focus and latus rectum.

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

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. The area of the equilateral triangle inscribed in the curve C having one vertex as the vertex of curve C is

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

three normals are drawn from the point (14,7) to the curve y^(2)-16x-8y=0. find the co- ordinates of the feet of the normals.

Three normals are drawn from the point (7, 14) to the parabola x^(2)-8x-16y=0. Find the coordinates of the feet of the normals.