`T P` and `T Q` are tangents to the parabola `y^2=4a x` at `Pa n dQ ,` respectively. If the chord `P Q` passes through the fixed point `(-a ,b),` then find the locus of `Tdot`

TP&TQ are tangents to the parabola,y^(2)=4ax at P and Q. If the chord passes through the point (-a,b) then the locus of T is

P and Q are two distinct points on the parabola,y^(2)=4x with parameters t and t_(1) respectively.If the normal at P passes through Q, then the minimum value of t_(1)^(2) is

From a point, P perpendicular PM and PN are drawn to x and y axes, respectively. If MN passes through fixed point (a,b), then locus of P is

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.

If the angle between the normal to the parabola y^(2)=4ax at point P and the focal chord passing through P is 60^(@) , then find the slope of the tangent at point P.

If from a variable point 'P' on the line 2x-y-1=0 pair of tangent's are drawn to the parabola x^(2)=8y then prove that chord of contact passes through a fixed point,also find that point.

If a tangent to the parabola y^(2)=4ax meets the x -axis at T and intersects the tangents at vertex A at P, and rectangle TAPQ is completed,then find the locus of point Q.

A variable tangent to the parabola y^(2)=4ax meets the parabola y^(2)=-4ax P and Q. The locus of the mid-point of PQ, is

If tangent at P and Q to the parabola y^(2)=4ax intersect at R then prove that mid point the parabola,where M is the mid point of P and Q.