If `S` be the focus of the parabola and tangent and normal at any point `P` meet its axis in `T and G` respectively, then prove that `ST=SG = SP`.

The tangent PT and the normal PN to the parabola y^2=4ax at a point P on it meet its axis at points T and N, respectively. The locus of the centroid of the triangle PTN is a parabola whose:

The tangent and normal at any point P of an ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 cut its major axis in point Q and R respectively. If QR=a prove that the eccentric angle of the point P is given by e^(2)cos^(2)phi+cosphi-1=0

Tangent PT and normal PN to the parabola y^(2)=4ax at a point P on it meet its axis at T and N respectively. The Locus of the centroid of the triangle PTN is a parabola whose

The ordinate and the normal at any point P on the curve meet the x-axis at points A and B respectively. Find the equation of the family of curves satisfying the condition , The product of abscissa of P and AB =arithmetic mean of the square of abscissa and ordinate of P .

The tangents to the parabola y^2=4a x at the vertex V and any point P meet at Q . If S is the focus, then prove that S PdotS Q , and S V are in GP.

The tangents to the parabola y^2=4a x at the vertex V and any point P meet at Q . If S is the focus, then prove that S PdotS Q , and S V are in GP.

The tangent drawn at any point of the curve sqrtx+sqrty = sqrta meets the OX and OY axes at points P and Q respectively, prove that OP+OQ = a.

The tangent and normal at P(t) , for all real positive t , to the parabola y^2= 4ax meet the axis of the parabola in T and G respectively, then the angle at which the tangent at P to the parabola is inclined to the tangent at P to the circle passing through the points P, T and G is

If the diameter through any point P of a parabola meets any chord in A and the tangent at the end of the chord meets the diameter in B and C, then prove that PA^2=PB.PC

If (-2,5) and (3,7) are the points of intersection of the tangent and normal at a point on a parabola with the axis of the parabola, then the focal distance of that point is