Question

If the product of power of point (1, 1) and (–1, –1) with respect to circle $x^2+y^2+2px+2qy+4=0$ is negative and the circle neither touches nor intersects co-ordinate axes, then the area of region formed by the set of ordered pair (p, q) on pq plane is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is A

1

$(2p+2q+6)(–2p–2q+6)<0\Rightarrow (p+q+3)(p+q–3)>0$
Also $p^2<4\Rightarrow pϵ(-2,2)$
And $q^2<4\Rightarrow qϵ(-2,2)$
$\therefore Area=2\times \frac{1}{2}\times 1=1$