If the point $(\lambda, l+\lambda)$ lies inside the circle $x^2+y^2=1$, then
If the point $(\lambda, l+\lambda)$ lies inside the circle $x^2+y^2=1$, then
- $\lambda>0$
- $\lambda < 0$
- $-1 < \lambda < 0$
- $0 < \lambda < 1$
Solution
$(\lambda, 1+\lambda)$ lie inside the $x^2+y^2=1$
$\therefore \quad(\lambda)^2+(1+\lambda)^2-1 < 0$
$\Rightarrow \lambda^2+1+2 \lambda+\lambda^2-1 < 0$
$\Rightarrow \quad 2 \lambda^2+2 \lambda < 0 \Rightarrow 2 \lambda(\lambda+1) < 0$
$\therefore \quad-1 < \lambda < 0$
Asked in: AP EAMCET 2021 (24 Aug Shift 2)
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