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. $\lambda <5$
• B. $\lambda <\frac{-57}{5}$
• C. $\lambda >5$
• D. $\lambda <11$

Answer 1

The correct option is B

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

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

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

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

$\Rightarrow 5\lambda +57<0$

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