Shared asymptotes Suppose that two hyperbolas with eccentricities e and E have perpendicular major axes and share a set of asymptotes. Show that e?2 + E?2 = 1.

Solution 89AEStep 1:We have given two hyperbolas with eccentricities e and E have perpendicular major axes and share a set of asymptotesWe have to show that Step 2:Two hyperbolas have perpendicular major axesSo the product of major axes two hyperbolas should be -1 that is if one hyperbola is As we know the result If & are the eccentricities of the hyperbola & its conjugate then = 1