is this right?

At how many points do the graphs of
x^2/4 + y^2/9 = 1 and
x^2/4 - y^2/9 = 1
intersect?


is the answer 4?

4 at most. Now prove it.

Hello, jaredroy23!

Did you try anything?

At how many points do the graphs of \(\displaystyle \,\frac{x^2}{4}\,+\,\frac{y^2}{9}\:=\;1\,\) and \(\displaystyle \,\frac{x^2}{4}\,-\,\frac{y^2}{9}\:=\:1\,\) intersect?

Click to expand...

To find intersections, solve the system!

We have: . \(\displaystyle \begin{array}{ccc}\frac{x^2}{4}\,+\,\frac{y^2}{4}\:=\:1\\ \\ \frac{x^2}{4}\,-\,\frac{y^2}{4}\:=\:1\end{array}\)

Add the equations: .\(\displaystyle 2\cdot\frac{x^2}{4}\:=\:2\;\;\Rightarrow\;\;x^2\,=\,4\;\;\Rightarrow\;\;x\,=\,\pm2\)

We have only two intersections.