The tangent to y² = ax makes an angle 45⁰ with x- axis. Then its point of contact is

Through the vertex O of the parabola y² = 4ax a perpendicular is drawn to any tangent meeting it at P and the parabola at Q.Then OP.OQ =

The locus of the point of intersection of two tangents to the parabola y² = 4ax which make complementary angles wit the axis of the parabola is

If the distance of two points P and Q on the parabola y² = 4ax are 4 and 9 respectively,then 9  respectively,then the distance of the point of intersection of the tangents at P and Q fro the focus is

The line y = m(x + a)+a/m touch the parabola y²= 4a(x+ a) form

If the line x + y + 2 = 0 touches the parabola y² = kx, then k =

The point of contact of  2x – y + 2 = 0 to the parabolay² = 16x is

If the tangents and normals at the extremities of a focal chord of a parabola intersect at (x₁,y₁) and (x₂,y₂) respectively, then

the equation of the parabola whose vertex is at (0,0) and focus is the point of intersection of x+y  =2, 2x –y = 4 is

The locus of the point of intersection of the perpendicular tangents to the parabola x² = 4ay is