Normal to an ellipse

JEE Main Mathematics · Ellipse · 3 questions, latest first

• If the radius of the largest circle with centre (2,0) inscribed in the ellipse x^2+4 y^2=36 is r, then 12 r^2 is equal to202311 April, Shift 2 · Q14
• If the maximum distance of normal to the ellipse x^2/4+y^2/b^2=1, b<2, from the origin is 1, then the eccentricity of the ellipse…202331 January, Shift 1 · Q74
• Let C be the largest circle centred at (2,0) and inscribed in the ellipse x^2/36+y^2/16=1. If (1, α) lies on C, then 10 α^2 is…202324 January, Shift 1 · Q89