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

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

The slope of the tangent to the parabola y^(2)=4ax at the point (at^(2), 2at) is -

A tangent to the hyperbola x^(2)-2y^(2)=4 meets x-axis at P and y-aixs at Q. Lines PR and QR are drawn such that OPRQ is a rectangle (where O is origin).Find the locus of R.

The angle between tangents to the parabola y^2=4ax at the points where it intersects with teine x-y-a = 0 is (a> 0)

Tangent and normal drawn to a parabola at A(a t^2,2a t),t!=0 meet the x-axis at point B and D , respectively. If the rectangle A B C D is completed, then the locus of C is

The tangent at any point P onthe parabola y^2=4a x intersects the y-axis at Qdot Then tangent to the circumcircle of triangle P Q S(S is the focus) at Q is

y=x is tangent to the parabola y=ax^(2)+c . If c=2, then the point of contact is

y=x is tangent to the parabola y=2ax^(2)+c . If (1,1) is the point of contact, then a is

A tangent is drawn to the parabola y^2=4a x at P such that it cuts the y-axis at Qdot A line perpendicular to this tangents is drawn through Q which cuts the axis of the parabola at R . If the rectangle P Q R S is completed, then find the locus of Sdot .

If a tangent to the parabola y^2 = 4ax intersects the x^2/a^2+y^2/b^2= 1 at A and B , then the locus of the point of intersection of tangents at A and B to the ellipse is