The abscissae of two points \(P, Q\) are the roots of the equation \(2 x^2+4 x-7=0\) and their ordinates are…
The abscissae of two points \(P, Q\) are the roots of the equation \(2 x^2+4 x-7=0\) and their ordinates are the roots of the equation \(3 x^2-12 x-1=0\). Then the centre of the circle with \(P Q\) as a diameter is
\((-1,2)\)
\((-2,6)\)
\((1,-2)\)
\((2,-6)\)
Solution
Since, it is given that abscissae of two point \(P, Q\) are roots of the equation \(2 x^2+4 x-7=0\) and their ordinates are the roots of the equation \(3 x^2-12 x-1=0\). Let \(P\left(x_1, y_1\right)\) and \(Q\left(x_2, y_2\right)\), then
\(x_1+x_2=-2 \text { and } y_1+y_2=4\)
Now, centre of the circle with \(P Q\) as a diameter is
\(\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)=(-1,2) \text {. }\)
Hence, option (1) is correct.