The point of contact of 2x-y+2 =0 to the parabola `y^(2)=4ax` is

The point of contact of the line x-2y-1=0 with the parabola y^(2)=2(x-3) , is

The mid-point of the chord 2x+y-4=0 of the parabola y^(2)=4x is

The point of contact of 9x+8y-11=0 to the hyperbola 3x^(2)-4y^(2)=11 is

Let the tangents PQ and PR are drawn to y^(2)=4ax from any point P on the line x+4a=0 . The angle subtended by the chord of contact QR at the vertex of the parabola y^(2)=4ax is

Prove that the portion of the tangent intercepted,between the point of contact and the directrix of the parabola y^(2)= 4ax subtends a right angle at its focus.

The locus of the point of intersection of two tangents to the parabola y^(2)=4ax which make complementary angles with the axis of the parabola is

The locus of the poles of tangents to the parabola y^(2)=4ax with respect to the parabola y^(2)=4ax is

The sum of the ordinates of point of contacts of the common tangent to the parabolas y = x^2 + 4x +8 and y=x^2+8x +4 is

The locus of the middle points of normal chords of the parabola y^2 = 4ax is-

The point of contact 8x-9y+5 = 0 with the ellipse 4x^(2)+9y^(2)=1 is