Graph$25y^2-9x^2=225.$

Here equation of hyperbola is $25y^2-9x^2=225.$

We need to plot the graph of hyperbola.

Given equation is $25y^2-9x^2=225$.

To convert into the standard form we have to divide the equation by 225.Then given equation becomesrole="math" localid="1645601754272" $$\begin{gathered} \frac{25y^2}{225}-\frac{9x^2}{225}=\frac{225}{225} \\ \frac{y^2}{9}-\frac{x^2}{25}=1,thisisthes\tan dardformofthegivenequation. \end{gathered}$$

Here hyperbola in standard form is .$\frac{y^2}{9}-\frac{x^2}{25}=1$.

Here term y² is positive, the transverse axis is vertical. Since a² =9 so $a=\pm 3$.The vertices are on the y-axis,

(0, −a), (0, a) are(0,-3) and( 0,3).Since b²=25 then $b=\pm 5$.

The rectangle intersects the x-axis at (−5, 0), (5, 0) and the y-axis at the vertices. Draw the asymptotes through the diagonals of the rectangle. Now we can draw the two branches of the hyperbola.

Here graph of$\frac{y^2}{9}-\frac{x^2}{25}=1$is given below