If the segment intercepted by the parabola `y^2=4a x` with the line `l x+m y+n=0` subtends a right angle at the vertex, then (a) `4a l+n=0` (b) `4a l+4a m+n=0` (c) `4a m+n=0` (d) `a l+n=0`

Find the locus of the middle points of the chords of the parabola y^2=4a x which subtend a right angle at the vertex of the parabola.

Tangents are drawn to the parabola y^2=4a x at the point where the line l x+m y+n=0 meets this parabola. Find the point of intersection of these tangents.

A square has one vertex at the vertex of the parabola y^2=4a x and the diagonal through the vertex lies along the axis of the parabola. If the ends of the other diagonal lie on the parabola, the coordinates of the vertices of the square are (a) (4a ,4a) (b) (4a ,-4a) (c) (0,0) (d) (8a ,0)

The locus of the midpoint of the segment joining the focus to a moving point on the parabola y^2=4a x is another parabola with directrix (a) y=0 (b) x=-a (c) x=0 (d) none of these

Tangents are drawn from any point on the line x+4a=0 to the parabola y^2=4a xdot Then find the angle subtended by the chord of contact at the vertex.

If y=m_1x+c and y=m_2x+c are two tangents to the parabola y^2+4a(x+c)=0 , then

If A_n be the area bounded by the curve y=(tanx)^n and the lines x=0,\ y=0,\ x=pi//4 , then for n > 2.

If the area of the rhombus enclosed by the lines l x+-m y+-n=0 is 2 sq. units, then, a) l,m,n are in G.P b) l,n,m are in G.P. c) lm=n d) ln=m

Identify the orbital with n=4 and l=0.

Let L be a normal to the parabola y^2=4x dot If L passes through the point (9, 6), then L is given by (a) y-x+3=0 (b) y+3x-33=0 (c) y+x-15=0 (d) y-2x+12=0