Question

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

Short answer

Graph of$25y^2-9x^2=225$is given below

Step-by-step solution

Step 1. Given information

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

We need to plot the graph of hyperbola.

Step 2. Converting into a standard form 

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" $$\begin{gathered} \frac{25y^2}{225}-\frac{9x^2}{225}=\frac{225}{225} \\ \frac{y^2}{9}-\frac{x^2}{25}=1,thisisthes\tan dardformofthegivenequation. \end{gathered}$$

Step 3. Description About sketching graph 

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.

Step 4. Sketching the graph 

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