The points on the curve $\mathrm{y}={\mathrm{x}}^2+\sqrt{1-{\mathrm{x}}^2}$ at which the normal is parallel to x-axis are

The given curve is $\mathrm{y}={\mathrm{x}}^2+\sqrt{1-{\mathrm{x}}^2}$

Differentiate both sides with respect to $x$

$\frac{dy}{dx}=2x+\frac{1}{2\sqrt{1-x^2}}\left(-2x\right)$

SInce the normal to the curve is parallel to $x$ axis, it means tangent is parallel to $y-$ axis

It implies that $1-x^2=0\Rightarrow x=\pm 1$

Hence, $y=1+0=1$

Therefore, the required points are $\left(\pm 1,1\right)$