Question

The abscissae of two points $P,Q$ are the roots of the equation $2x^2+4x-7=0$ and their ordinates are the roots of the equation $3x^2-12x-1=0$. Then the centre of the circle with $PQ$ as a diameter is

• A. (-1, 2)
• B. (-2, 6)
• C. (1, -2)
• D. (2, -6)

Answer 1

Answer: (A)

Since, it is given that abscissae of two point $P,Q$ are roots of the equation $2x^2+4x-7=0$
and their ordinates are the roots of the equation
$3x^2-12x-1=0$. Let $P\left(x_1,y_1\right)$
and $Q\left(x_2,y_2\right)$, then $x_1+x_2=-2$ and $y_1+y_2=4$
Now, centre of the circle with $PQ$ as a diameter is
$\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)=(-1,2)$