Answer
$(0.7071,0.7071), (0.7071,-0.7071) $
Work Step by Step
The line $x=\frac{\sqrt{2}}{2}$ intersects the circle $x^2+y^2=1$ at $(0.7071,0.7071)\,$and$\,(0.7071,-0.7071)$ as can be seen from the figure.
The solution can also be obtained analytically by substituting $x=\frac{\sqrt{2}}{2}$ in the equation $x^2+y^2=1$ and solving for $y$ $$y^2 = 1-x^2$$ $$y = \pm \sqrt{1-x^2} = \pm \sqrt{1-(\frac{\sqrt{2}}{2})^2} = \pm \sqrt{0.5}$$ $$\therefore y = \pm \frac{\sqrt{2}}{2} \approx \pm 0.7071$$ $\therefore $ The coordinates are $(0.7071,0.7071)\,$and$\,(0.7071,-0.7071)$.
