Two equal parabolas have the same vertex and their axes are at right angles. Prove that their commom tangent touches each at the end of a latus rectum.

Two equal parabolas have the same vertex and their axes are at right angles. Prove that their common tangent touches each at the end of their latus recta.

Two equal parabolas have the same vertex and their axes are at right angles. The length of the common tangent to them, is

Two equal parabola have the same vertex and their axes are at right angles. Prove that they cut again at an angle tan^(-1) 3/4 .

Find the equations of the tangent and normal to the parabola y^(2) =6x at the positive end of the latus rectum

Find the area of the triangle formed by the lines joining the vertex of the parabola x^(2) = 8y to the ends of its latus rectum.

Two parabolas with a common vertex and with axes along x-axis and y-axis respectively, intersect each other in the first quadrant. If the length of the latus rectum of each parabola is 3, then the equation of the common tangent to the two parabolas is:

Find the area of the triangle formed by the lines joining the vertex of the parabola y^(2) = 16x to the ends of the latus rectum.

Find the area of the triangle formed by the lines joining the vertex of the parabola x^(2) = -8y to the ends of its latus rectum.

Find the area of the triangle formed by the lines joining the vertex of the parabola x^2 = - 36y to the ends of the latus rectum.

Find the area of the triangle formed by the lines joining the vertex of the parabola x^2=12 y to the ends of its latus-rectum.