Question

If the point $(a,a+1)$ belongs to the interior of the region bounded curve $y=\sqrt{5-x^2}$ and the x-axis then a belongs to

• A. $(-2,1)$
• B. $(-1,1)$
• C. $(-2,0)$
• D. $(0,1)$

Answer 1

The correct option is A $(-2,1)$

Given curve is clearly a circle, $x^2+y^2=5$
For $(a,a+1)$ to be interior point of the given curve,
$a^2+(a+1{)}^2<5$
$\Rightarrow 2a^2+2a-4<0$
$\Rightarrow a^2+a-2<\Rightarrow (a-1)(a+2)<0$
$\Rightarrow aϵ(-2,1)$