Question

If the point $(k+1,k)$ lies inside the region bounded by the curve and y-axis, then $k$ belongs to the interval $x=\sqrt{25-y^2}$

• A. $(-1,3)$
• B. $(-4,3)$
• C. $(-\infty ,-4)\cup (3,\infty )$
• D. none of these

Answer 1

The correct option is A $(-1,3)$

Since the point $(k+1,k)$ lies inside the region bounded by $x=\sqrt{25-y^2}$ and y-axis,

$\therefore {(k+1)}^2+k^2-25<0$ and $k+1>0$

$\Rightarrow 2k^2+2k-24<0$ and $k>-1$

$\Rightarrow k^2+k-12<0$ and $k>-1$

$\Rightarrow (k+4)(k-3)<0$ and $k>-1$

$\Rightarrow -4<k<3$ and $k>-1$

$\Rightarrow -1<k<3$