Ellipse Director circle 5 selected practice problems : Details in description

Problem 1: Find the length of sides of square made by four perpendicular tangents to ellipse x^2/7+2y^2/11=1?
Problem 2: If the ellipse x^2/(a^2-7)+y^2/(13-5a)=1 is inscribed in a square of length 2^1/2a, find a?
Problem 3: If the tangents PQ and PR from the circle x^2+y^2=25 to the ellipse x^2/16+y^2/b^2=1 so that PQSR lie on circumcircle of PQR, find e?
Problem 4: From a point perpendicular tangents are drawn to ellipse x^2+2y^2=2. The chord of contact touches a concentric circle. Find the ratio of minimum and maximum area of the circle?
Problem 5: Number of points on ellipse x^2/50+y^2/20=1 from which perpendicular tangents can be drawn to ellipse x^2/16+y^2/9=1 Support the channel:
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