Let the abscissae of the two points P and Q be the roots of 2x² - rx + p = 0 and the ordinates of P and Q be the roots of x² - sx - q = 0. If the equation of the circle described on PQ as diameter is 2(x² + y²) - 11x - 14y - 22 = 0, then 2r + s - 2q + p is equal to _ _ _ _ _.

Coordinate Geometry: JEE Main 2022 Mathematics question

JEE Main 2022 · 25 Jun, Morning shift · Q29

JEE Main 202225 Jun, Morning shiftMathematicsMediumCoordinate Geometry478× since 2002

Let the abscissae of the two points P and Q be the roots of

2{x^2} - rx + p = 0

and the ordinates of P and Q be the roots of

{x^2} - sx - q = 0

. If the equation of the circle described on PQ as diameter is

2({x^2} + {y^2}) - 11x - 14y - 22 = 0

, then

2r + s - 2q + p

is equal to __________.

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