Question

Let $P(x_1,y_1)$ and $Q(x_2,y_2)$ are two points such that their abscissa $x_1$ and $x_2$ are the roots of the equation $x^2+2x-3=0$ while the ordinates $y_1$ and $y_2$ are the roots of the equation $y^2+4y-12=0.$ The centre of the circle with PQ as diameter is

• A. (-1, -2)
• B. (1, 2)
• C. (1, -2)
• D. (-1, 2)

Answer 1

The correct option is A (-1, -2)

$x_1,x_2$ are roots of $x^2+2x+3=0$
$\Rightarrow x_1+x_2=-2$
$\therefore \frac{x_1+x_2}{2}=-1$

$y_1,y_2$ are roots of $y^2+4y-12=0$
$\Rightarrow y_1+y_2=-4\Rightarrow \frac{y_1+y_2}{2}=-2$
Centre of circle $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(-1,-2).$