# What is the slope of the tangent line of x^2 + y^2 = 1/2  at x=1?

Dec 9, 2015

There is no point on the graph with $x = 1$, so there is no tangent line at $x = 1$.

#### Explanation:

For ${x}^{2} + {y}^{2} = \frac{1}{2}$, if $x = 1$, then ${y}^{2} = - \frac{1}{2}$.
There is no real $y$ that solves this.

Geometrically

The graph of ${x}^{2} + {y}^{2} = \frac{1}{2}$ is a circle of radius $\frac{\sqrt{2}}{2}$.

The maximum $x$ value on that circle is $x = \frac{\sqrt{2}}{2} \approx 0.7071$.