Use calculus to find a value for the $($unknown$)$ constant $k$ so that the parabola $y=x^2+k$ is tangent to the unit circle at $2$ points $($as shown in diagram$).$

Recall that the unit circle is described by the equation $x^2+y^2=1.$

It will help to know that the circle and the parabola must share a tangent line at each intersection point.

Hints:

Find a formula for $\frac{dy}{dx}$ for each curve separately.

At the point of intersection, the curves must share the same tangent slope, and this will help you set up an equation to find the $y-$coordinate first.