Angle between the parabolas `y^2=4b(x-2a+b)` and `x^2+4a(y-2b-a)=0` at the common end of their latus rectum , is:

The normal to y^(2)=4a(x-a) at the upper end of the latus rectum is

Find the angle between the parabolas y^2=4a x and x^2=4b y at their point of intersection other than the origin.

If the line y=x-1 bisects two chords of the parabola y^(2)=4bx which are passing through the point (b, -2b) , then the length of the latus rectum can be equal to

[" The parabola " y^(2)=2ax " passes through the centre of the circle " 4x^(2)+4y^(2)-8x+12y-7=0 then the area of the " Delta^(Lc)AL_(1)L_(2) is (where "A" is the vertex of the parabola and " L_(1) " and " L_(2) are the end points of the latus rectum)

Find the equation of the normal to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at the positive end of the latus rectum.

The directrix of a parabola is 2x-y=1. The focus lies on y-axis.The locus of one end of the latus rectum is

The circle described on the line joining the foci of the hyperbola (x^(2))/(16)-(y^(2))/(9) = 1 as a diameter passes through an end of the latus rectum of the parabola y^(2) = 4ax , the length of the latus rectum of the parabola is

If y=mx+4 is common tangent to parabolas y^(2)=4x and x^(2)=2by . Then value of b is

The point of intersection of the normals to the parabola y^(2)=4x at the ends of its latus rectum is