Question

In the following exercises, graph

$\frac{{\left(x+2\right)}^2}{4}-\frac{{\left(y-1\right)}^2}{9}=1$

Short answer

The graph is

Step-by-step solution

Step 1. Given information

The equation is $\frac{{\left(x+2\right)}^2}{4}-\frac{{\left(y-1\right)}^2}{9}=1$.

Step 2. Calculation.

The x² term is positive, the transverse axis is horizontal.

The hyperbola opens left and right.

Find the centre from the equation.

Compare the equation with the standard form.

$\frac{{\left(x-h\right)}^2}{a^2}-\frac{{\left(y-k\right)}^2}{b^2}=1$

So, $\left(h,k\right)=\left(-2,1\right)$ and $a^2=4\Rightarrow a=\pm 2$ and localid="1645724144236" $b^2=9\Rightarrow b=\pm 3$

Sketch the rectangle that goes through the points 2 unit left/right of the centre 3 units above/ below the centre.

Step 3. Draw the graph.

Sketch the asymptotes and draw the graph