Question

a tangent to the ellipse x2 + 4y2=4 meets the ellipse x2+2y2=6 at P and Q.the angle between the tangents at P and Q of the ellipse x2 +2y2=6

Answer 1

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