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A tangent to the ellipse x 2 +4y 2 =4 meets the ellipse x 2 +2y 2 =6 at P &Q.The angle b/w the tangents at P & Q of ellipse x 2 +2y 2 =6 is......

A tangent to the ellipse x2 +4y2=4 meets the ellipse x2+2y2=6 at P &Q.The angle b/w the tangents at P & Q of ellipse  x2+2y2=6 is......

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1 Answers

askIITians Faculty 69 Points
6 years ago
Draw the 2 ellipse in the figure. At a point(take for instance (0,1) for convenience and symmtry), draw a tangent to the first ellipse cutting the second at 2 points. As we know the slpoe of tangent and also a point through which it passes, calculate the eqn of tangent. Calculate the points of intersection of tangent with the second elipse. Calculate the derivative of this ellipse at these points to obtain their slope at these points. This gives the slope of tangents at these points. Hence, calculate the angle by using these 2 slopes.

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