Respuesta :
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).
Answer: Graph B
The first graph is going up and the second one is going down.
