Question

Find the value of λ if the point (3, 5) lies inside the circle $x^2+y^2+6x+\lambda y+5=0$

• A. λ< 5
• B. λ<-57/5
• C. λ>5
• D. λ<11

Answer 1

The correct option is B

λ<-57/5

If (3, 5) lies inside the circle, then $S_1$ will be less than zero

$S_1\equiv 3^2+5^2+3\times 6+5\lambda +5<0$

$\Rightarrow 9+25+18+5\lambda +5<0$

$\Rightarrow 5\lambda +57<0$

$\Rightarrow \lambda <\frac{-57}{5}$