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QJEEM22Maf7d9: JEE Main 2022 Mathematics - Class 11 JEEM22Maf7d9 Solution: Let the abscissae of the two points P and Q on a circle be the…

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 $P$ and $Q$ be the roots of $y^{2} + 2 y - 7 = 0$ . If $PQ$ 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 _____________.

Multiple Choice Options

A 12
B 13
C 14
D 16

Step-by-Step Verified Solution

Abscissae of PQ are roots of $x^{2} - 4 x - 6 = 0$

Ordinates of PQ are roots of $y^{2} + 2 y - 7 = 0$

and PQ is diameter

$\Rightarrow$ Equation of circle is

$x^{2} + y^{2} - 4 x + 2 y - 13 = 0$

But, given $x^{2} + y^{2} + 2 a x + 2 b y + c = 0$

By comparison $a = - 2, b = 1, c = - 13$

$\Rightarrow a + b - c = - 2 + 1 + 13 = 12$

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