QuestionFind all points of intersection of the given curves. Make a sketch of the curves that shows the points of intersection. $$x^{2}+y^{2}=5 \text { and } x^{2}-y^{2}=1$$

Studdy Solution
Sketch the curves:
- Draw the circle $x^2 + y^2 = 5$ centered at the origin with radius $\sqrt{5}$. - Draw the hyperbola $x^2 - y^2 = 1$ with its transverse axis along the x-axis. - Mark the points of intersection: $(\sqrt{3}, \sqrt{2})$, $(\sqrt{3}, -\sqrt{2})$, $(- \sqrt{3}, \sqrt{2})$, $(- \sqrt{3}, -\sqrt{2})$.
The points of intersection are:
$$(\sqrt{3}, \sqrt{2}), (\sqrt{3}, -\sqrt{2}), (-\sqrt{3}, \sqrt{2}), (-\sqrt{3}, -\sqrt{2})$$