How do you graph #12y^2-25x^2=300# and identify the foci and asympototes?
1 Answer
The foci are
The asymptotes are
Explanation:
First, we see turn the equation so that it equals one.
You can simplify this to:
Remember that a hyperbolic equation can be in two forms:
Now, a graph of a hyperbola opens to the left and the right when
Also, a graph of a hyperbola opens to up and down when
Because of this, the foci of a hyperbola is
Similarly, the foci of a hyperbola is
The equation for the asymptote of a hyperbola is
Similarly, the equation for the asymptote of a hyperbola is
Since
Therefore, the foci are
The asymptotes are
I have a graph from desmos.com here to visualize it.