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

The two waves of the same frequency moving in opposite direction give rise to

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 .

A is a point (a,b) in the first quadrant.If the two circles which passes through A and touches the coordinate axes cut at right angles then:

Two parabolas have the same focus. If their directrices are the x-axis & the y-axis respectively, then the slope of their common chord is

Two unequal parabolas have the same common axis which is the x-axis and have the same vertex which is the origin with their concavities in opposite direction.If a variable line parallel to the common axis meet the parabolas in P and P' the locus of the middle point of PP' is

If two isosceles triangles have a common base, prove that the line segment joining their vertices bisects the common base at right angles.

Two parabola have the same focus.If their directrices are the x-axis and the y-axis respectively,then the slope of their common chord is: