Question

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

• A. $13$
• B. $12$
• C. $14$
• D. $16$

Answer 1

The correct option is B $12$

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

Ordinates of $PQ\text{are roots of:}{x}^2+2x-7=0$
and $PQ$ is diameter

$\therefore$ Equation of circle is $x^2+y^2-4x+2y-13=0$

​​​​​​But, given $x^2+y^2+2ax+2by+c=0$

By comparison $a=–2,b=1,c=–13$​​​​​​
$\Rightarrow a+b-c=-2+1+13=12$