Ellipse-Ellipse interaction: Selected 5 practice questions Level 3 (details in description)

Ellipse-Ellipse interaction: Selected 5 practice questions Level 3 (details in description) Example 1: If two concentric ellipse be such that each pass through focii of other and e1 and e2 are their eccentricities and they have same major axis, find the angle between their axis? Example 2: Ellipse E1 x^2/ 9+y^2/4=1 is inscribed in a rectangle R, which in turn is inscribed in another ellipse E2 which passes though (0,4), find equation of E2? Example 3: Find the equation of circle passing through points of intersection of ellipse x^2+2y^2--6x-12y+23=0 and 4x^2+2y^2--20x-12y+35=0? Example 4: Ellipse x^2+4y^2=4 is inscribed in a rectangle , which in turn is inscribed in another ellipse which passes though (4,0), find equation of the second ellipse? Example 5: A ladder 12 units long slides along perpendicular lines, find the eccentricity of locus of the point 4 units from its foot? Support the channel: UPI link: 7906459421@okbizaxis UPI Scan code: https://mathsmerizing.com/wp-content/... PayPal link: paypal.me/mathsmerizing