Find the points of contact `Q` and `R` of a tangent from the point `P(2,3)` on the parabola `y^2=4xdot`

P & Q are the points of contact of the tangents drawn from the point T to the parabola y^(2) = 4ax . If PQ be the normal to the parabola at P, prove that TP is bisected by the directrix.

Length of the chord of contact drawn from the point (-3,2) to the parabola y^(2)=4x is

If the chord of contact of tangents from a point P to the parabola y^(2)=4ax touches the parabola x^(2)=4by, then find the locus of P.

Find the area of the triangle formed by the tangents from the point (4,3) to the circle x^(2)+y^(2)=9 and the line joining their points of contact.

Find the locus of point P, if two tangents are drawn from it to the parabola y ^(2) = 4x such that the slope of one tangent is three times the slope of other.

Tangents are drawn from the points on a tangent of the hyperbola x^(2)-y^(2)=a^(2) to the parabola y^(2)=4ax. If all the chords of contact pass through a fixed point Q, prove that the locus of the point Q for different tangents on the hyperbola is an ellipse.

The chord of contact of tangents from three points P, Q, R to the circle x^(2) + y^(2) = c^(2) are concurrent, then P, Q, R

Find the locus of the middle points of the chords of contact of orthogonal tangents of the parabola y^(2)=4ax .

If the normals at two points P and Q of a parabola y^2 = 4x intersect at a third point R on the parabola y^2 = 4x , then the product of the ordinates of P and Q is equal to