Chord with a given midpoint and diameter

JEE Main Mathematics · Parabola · 4 questions, latest first

• Let the locus of the mid-point of the chord through the origin O of the parabola y^2=4 x be the curve S. Let P be any point on S.…202622 January, Shift 2 · Q12
• Let O be the vertex of the parabola x^2=4 y and Q be any point on it. Let the locus of the point P, which divides the line…202621 January, Shift 1 · Q12
• Let PQ be a chord of the parabola y^2=12 x and the midpoint of PQ be at (4,1). Then, which of the following point lies on the…20244 April, Shift 2 · Q15
• Let P(α, β) be a point on the parabola y^2=4 x. If P also lies on the chord of the parabola x^2=8 y whose mid point is (1, 5/4),…202429 January, Shift 2 · Q29