Question

In the following exercises, graph$\frac{{\left(x-3\right)}^2}{25}-\frac{{\left(y+2\right)}^2}{9}=1$

Short answer

The graph of equation $\frac{{\left(x-3\right)}^2}{25}-\frac{{\left(y+2\right)}^2}{9}=1$is as below

Step-by-step solution

Step 1. Given information

The equation is$\frac{{\left(x-3\right)}^2}{25}-\frac{{\left(y+2\right)}^2}{9}=1$

Draw the graph.

Step 2. Calculation

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

The hyperbola opens left and right .

Find the centre

Compare the equation with standard form $\frac{{\left(x-h\right)}^2}{a^2}-\frac{{\left(y-k\right)}^2}{b^2}=1$

So, $\left(h,k\right)=\left(3,-2\right)$ and $a^2=25\Rightarrow a=\pm 5$and $b^2=9\Rightarrow b=\pm 3$

Sketch the rectangle that goes through the points 5 units left/right of centre 3 units above/ below the centre.

Step 3. Draw the graph

Sketch the asymptotes and draw the graph