Graph$4y^2-25x^2=100$

Here given equation for a hyperbola is $4y^2-25x^2=100$.

We have to sketch a graph of hyperbola

To write the equation in a standard form we have to divide by 100, then we get $$\begin{gathered} 4y^2-25x^2=100,dividingby100 \\ \frac{4y^2}{100}-\frac{25x^2}{100}=\frac{100}{100} \\ \frac{y^2}{25}-\frac{x^2}{4}=1 \end{gathered}$$

This is the standard form of the equation of hyperbola here.

Here hyperbola in standard form is $\frac{y^2}{25}-\frac{x^2}{4}=1$. The term y² is positive, the transverse axis is vertical. Since a² =25 so $a=\pm 5$.The vertices are on the y-axis,

(0, −a), (0, a) are(0,-5) and( 0,5).Since b²=4 then role="math" localid="1645600238300" $b=\pm 2$.

The rectangle intersecting the x-axis at

(−2, 0), (2, 0) and the y-axis at the vertices. Plot the asymptotes through the diagonals of the rectangle.

now we can draw the two branches of the hyperbola.

Here the standard form of the hyperbola is$\frac{y^2}{25}-\frac{x^2}{4}=1$. Graph is given below