What are the vertices of the hyperbola with equation 4y^2 - 25x^2 = 100?

Answer:(0,-5) and (0,5).Step-by-step explanation:We have been given that an equation of hyperbola [tex]4y^2-25x^2=100[/tex].First of all we will convert our given equation into the standard form of hyperbola.Let us divide both sides of our equation by 100.[tex]\frac{4y^2}{100}-\frac{25x^2}{100}=\frac{100}{100}[/tex][tex]\frac{y^2}{25}-\frac{x^2}{4}=1[/tex]Since we know that the positive term in the equation of a hyperbola determines whether the hyperbola opens in the x-direction or in the y-direction. Our hyperbola has a positive [tex]y^2[/tex] term, so it opens in the y-direction (up and down).  The equation of a vertical hyperbola is :[tex]\frac{y^2}{a^2}-\frac{x^2}{b^2}=1[/tex], where -a and a are vertices of our hyperbola. [tex]\frac{y^2}{5^2}-\frac{x^2}{2^2}=1[/tex] [tex]a^2=5^2[/tex][tex]5^2=\pm5[/tex]Upon comparing our equation with vertical hyperbola equation we can see that vertices of our hyperbola will be (0.-5) and (0,5).