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 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 .

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.

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

In the figure, two circles touch each other externally at C. Prove that the common tangent at C bisects the other two common tangents.

In the given figure two circles touch each other at the point C. Prove that the common tangent at P and Q.