Equation of tangent to parabola `y^2 = 4ax`

Find the locus of point of intersection of tangent to the parabola y^2=4ax which are inclined at an angle theta to each other.

Differential equation of all tangents to the parabola y^2=4ax is (A) y=mx+a/m , m!=0 (B) y_1(yy_1-x)=a (C) xy_1^2-yy_1+a=0 (D) none of these

T is a point on the tangent to a parabola y^(2) = 4ax at its point P. TL and TN are the perpendiculars on the focal radius SP and the directrix of the parabola respectively. Then

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.

The line 2y = ax+b is a tangent to parabola y^(2) = 4ax(a in N) , then for maximum value of [a+b/a] the value of 'a' is ({.] denotes the greates integer function)