If the length of the minor axis of an ellipse equals half the distance between its foci, find the eccentricity using c=2b and a²=b²+c².
An ellipse centred at (1,0) has latus rectum 1/2 and its minor axis subtends 60° at the foci. Find the square of the sum of its major and minor axis lengths.
Find the equation of the chord of the ellipse x²/25+y²/16=1 whose midpoint is (3,1), using the T=S₁ chord-of-midpoint formula.
Ellipse E and hyperbola H have the same distance between their foci (2√3), with a−A=2 and eccentricity ratio 1/3. Find the sum of their latus rectum lengths.
Given αx+βy=109 is the equation of a chord of x²/9+y²/4=1 with midpoint (5/2,1/2), find α+β using the T=S₁ chord-of-midpoint formula.
If the midpoint of a chord of the ellipse x²/9+y²/4=1 is (√2, 4/3), and the chord’s length is 2√α/3, then α is: (1) 18 (2) 22 (3) 26 (4) 20.
Let E1: x²/9+y²/4=1. Ellipses Ei share E1’s centre and eccentricity, with minor axis of Ei equal to major axis of Ei+1. Find (5/π)ΣAi.
Two ellipses with the same eccentricity, a given latus rectum product, and a known focal distance intersect at four points. A JEE Main 2025 area problem, solved.
Given only the midpoint of a chord of an ellipse, find its length using the T = S1 equation of a chord — a JEE Main 2025 conic sections problem, solved.