Let the abscissae of the two points P and Q on a circle be the roots of x²-4 x-6=0 and the ordinates of P and Q be the roots of y²+2 y-7=0. If PQ is a diameter of the circle x²+y²+2 a x+2 b y+c=0, then the value of (a+b-c) is _ _ _ _ _ _ _.

Coordinate Geometry: JEE Main 2022 Mathematics question

JEE Main 2022 · 26 Jul, Evening shift · Q3053

JEE Main 202226 Jul, Evening shiftMathematicsMediumCoordinate Geometry478× since 2002

Let the abscissae of the two points

P

and

Q

on a circle be the roots of

x^{2}-4 x-6=0

and the ordinates of

\mathrm{P}

and

\mathrm{Q}

be the roots of

y^{2}+2 y-7=0

. If

\mathrm{PQ}

is a diameter of the circle

x^{2}+y^{2}+2 a x+2 b y+c=0

, then the value of

(a+b-c)

is _____________.