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Conics Problem and Parametric Equations : Prove that Tangents of Two Ellipses are Perpendicular

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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.

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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.