Question

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

• A. 12
• B. 13
• C. 14
• D. 16

Answer 1

Answer: (A)

Equation of circle diameter form $\left( x - x _1\right)\left( x - x _2\right)+\left( y - y _1\right)\left( y - y _2\right)=0$
(where $x_1, x_2$ are the roots of $x^2-4 x-6=0$ and $y_1, y_2$ are the roots of $y^2+2 y-7=0$ ) $x^2+y^2-4 x+2 y-13=0$
Now,
Compare it with the given equation, we get $a =-2, b =1, c =-13$
Now
$a+b-c=12$