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
  1. $\lambda>0$
  2. $\lambda < 0$
  3. $-1 < \lambda < 0$
  4. $0 < \lambda < 1$

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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