I am trying to identifying the region represented by the equation:


I know that if it was a sum then it would be a circle but since it is a difference, how do I go about determining what type of region it is and how do I graph such equation?


Your equation can be rewritten as $\dfrac {x^2}{3^2}-\dfrac {y^2}{3^2}=1$

Equations of the form $\dfrac {(x-h)^2}{a^2}-\dfrac {(y-k)^2}{b^2}=1$ are hyperbolas centered at $(h, k)$.

This is the graph for your equation:

Notice how the vertices of the hyperbola are at $(\pm3, 0)$.


Hint: if $x$ and $y$ satisfy $x^2-y^2=9$, then either $y=\sqrt{x^2-9}$ or $y=-\sqrt{x^2-9}$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.