Question

If a rectangular hyperbola $(x-1)(y-2)=4$ cuts a circle $x^2+y^2-7x-9y+c=0$ at points $(3,4),(5,3),(2,6)$ and point $P(u,v)$, then the value of $9(u+v)$ is equal to

• A. $-8$
• B. $-9$
• C. $8$
• D. $9$

Answer 1

The correct option is B $-9$

We know that if a circle cuts a rectangular hyperbola, then A.M. of points of intersections is the mid point of centre of hyperbola and circle

$\frac{3+5+2+u}{4}=\frac{\frac{7}{2}+1}{2}\Rightarrow u=-1$

$\frac{4+3+6+v}{4}=\frac{\frac{9}{2}+2}{2}\Rightarrow v=0$

$9(u+v)=-9$