JEE 2020 Mathematics : Conic Section - 02

From a point P, perpendicular tangents PQ and PR are drawn to ellipse x² + 4y² = 4 . Locus of circumcentre of triangle PQR is

Let PQ be a chord of the ellipse , which subtends an angle of π/2 radians at the centre. If L is the foot of perpendicular from (0, 0) to PQ, then

If the foci of the ellipse  coincide with the foci of the hyperbola  then b² is equal to

The locus of the poles of normal chords of an ellipse is given by

If θ and Φ are eccentric angles of the ends of a pair of conjugate diameters of the ellipse , then θ - Φ is equal to