Question

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

Answer 1

Answer:

(0,-5) and (0,5).

Step-by-step explanation:

We have been given that an equation of hyperbola $4y^2-25x^2=100$.

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.

$\frac{4y^2}{100}-\frac{25x^2}{100}=\frac{100}{100}$

$\frac{y^2}{25}-\frac{x^2}{4}=1$

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 $y^2$ term, so it opens in the y-direction (up and down).  

The equation of a vertical hyperbola is :$\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$, where -a and a are vertices of our hyperbola.

$\frac{y^2}{5^2}-\frac{x^2}{2^2}=1$

$a^2=5^2$

$5^2=\pm5$

Upon comparing our equation with vertical hyperbola equation we can see that vertices of our hyperbola will be (0.-5) and (0,5).

Answer 2

Answer: Graph B

The first graph is going up and the second one is going down.