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Let the abscissae of the two points $\mathrm{\mathrm{P}}$ and $\mathrm{\mathrm{Q}}$ on a circle be the roots of $\mathrm{x^{2}-4 x-6=0}$ and the ordinates of $\mathrm{P}$ and $\mathrm{Q}$ be the roots of $\mathrm{y^{2}+2 y-7=0}$ . If $\mathrm{PQ}$ is a diameter of the circle $\mathrm{x^{2}+y^{2}+2 a x+2 b y+c=0}$ , then the value of $\mathrm{(a+b-c)}$ is _____________.
Option: 1
$12$

Option: 2
$13$

Option: 3
$14$

Option: 4
$16$

Answers (1)

best_answer

Equation of circle with PQ as diameter is

$\mathrm{x^{2}-4 x-6+y^{2}+2 y-7=0} \\$

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

$\mathrm{\therefore a=-2, b=1, c=-13} \\$

$\mathrm{\therefore a+b-c=12}$

Hence correct option is 1

Posted by

Ritika Jonwal

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