Chord with a given midpoint

JEE Main Mathematics · Ellipse · 6 questions, latest first

• Let x=9 be a directrix of an ellipse E, whose centre is at the origin and eccentricity is 1/3. Let P(α, 0), α>0, be a focus of E…20266 April, Shift 2 · Q12
• If α x+β y=109 is the equation of the chord of the ellipse x^2/9+y^2/4=1, whose mid point is (5/2, 1/2), then α+β is equal to:202529 January, Shift 2 · Q12
• If the midpoint of a chord of the ellipse x^2/9+y^2/4=1 is (√2, 4 / 3), and the length of the chord is (2 √α)/3, then α is:202528 January, Shift 2 · Q11
• The equation of the chord, of the ellipse x^2/25+y^2/16=1, whose mid-point is (3,1) is:202524 January, Shift 2 · Q13
• The length of the chord of the ellipse x^2/4+y^2/2=1, whose mid-point is (1, 1/2), is:202523 January, Shift 2 · Q9
• The length of the chord of the ellipse x^2/25+y^2/16=1, whose mid point is (1, 2/5), is equal to:202427 January, Shift 1 · Q16