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.

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

If three normals are drawn from the point (c, 0) to the parabola y^(2)= x , then-

The focal distance of a point on the parabola y^(2) = 8x is 4, find the coordinates of the point .

If normal are drawn from a point P(h , k) to the parabola y^2=4a x , then the sum of the intercepts which the normals cut-off from the axis of the parabola is (h+c) (b) 3(h+a) 2(h+a) (d) none of these

Prove that the focal distance of the point (x ,y) on the parabola x^2-8x+16 y=0 is |y-5|

Three normals are drawn from the point (c, 0) to the curve y^2 = x . Show that c must be greater than 1/2. One normal is always the axis. Find c for which the other two normals are perpendicular to each other.

The vertex of the parabola x^(2)+2y=8x-7 is

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

Tangent and normal are drawn at the point P-=(16 ,16) of the parabola y^2=16 x which cut the axis of the parabola at the points A and B , respectively. If the center of the circle through P ,A and B is C , then the angle between P C and the axis of x is

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