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

User Rchacko
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1 Answer

3 votes

Answer:

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

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.


(4y^2)/(100)-(25x^2)/(100)=(100)/(100)


(y^2)/(25)-(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 :
(y^2)/(a^2)-(x^2)/(b^2)=1, where -a and a are vertices of our hyperbola.


(y^2)/(5^2)-(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).

User Androyal
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