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 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.Prove that their common tangent touches each at the end of their latus recta.

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 .

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 .

Two parabolas have the same vertex and equal lengh of latus rectum such that their axes are at right angle. Prove that the common tangents touch each at the end of latus rectum.

Let A be the vertex and L the length of the latus rectum of the parabola,y^(2)-2y-4x-7=0 The equation of the parabola with A as vertex 2L the length of the latus rectum and the axis at right angles to that of the given curve is:

Prove that two parabolas having the same focus and their axes in opposite directions, cut at right angles.

A square is inscribed in an isosceles right triangle so that the square and the triangle have an angle common.Show that the vertex of the square opposite the vertex of the common angle bisects the hypotenuse

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: