The equations of two ellipses are i) 4x (squared) + 9y (squared) = 36 (ii) 2x (squared) + 3y (squared) = 30. A tangent to ellipse (i) meets the ellipse (ii) at the points P and Q. Show that the tangents at P and Q to ellipse (ii) are at right angles to one another. Please show this using parametric equations.
It is proven that the tangents of two ellipses are perpendicular. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.