Tangent curves in in the plane

Question

I need to find Formulas $c_1$ and $c_2: [-1,1] \to\mathbb{R}^2$ for the two curves and check tangency.

Figure 1.11

Basically I am stuck. Geometrically I understand both the curves. And I can solve either by itself. But I am having trouble getting everything to line up using the $[-1,1]$.

So they line up at the angle ${\pi\over 4}$ but I am having trouble normalizing the input $[-1,1]$ and making them line up

Answer 1

From the given informations it seems that

• $c_1$ is the circle: $x^2+y^2=1$
• $c_2$ is the line $y+x=\sqrt2$