Show that the length of the tangent to the parabola `y^2 = 4ax` intercepted between its point of contact and the axis of the parabola is bisected by the tangent at the vertex.

y=3x is tangent to the parabola 2y=ax^2+ab . If b=36,then the point of contact is

Show that the line x- y +4=0 is tangent to the parabola y^(2)= 16x . Find the point of contact.

Find all the curves y=f(x) such that the length of tangent intercepted between the point of contact and the x-axis is unity.

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.

Find the equation of tangent to the parabola y^(2)=8ax at (2a , 4a)

y=3x is tangent to the parabola 2y=ax^2+ab . If (2,6) is the point of contact , then the value of 2a is

The locus of the mid-point of the line segment joining a point on the parabola Y^(2)=4ax and the point of contact of circle drawn on focal distance of the point as diameter with the tangent at the vertex, is

Prove that the segment of tangent to xy=c^(2) intercepted between the axes is bisected at the point at contact .

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

For what values of 'a' will the tangents drawn to the parabola y^2 = 4ax from a point, not on the y-axis, will be normal to the parabola x^2 = 4y.