Mathematics, 26.06.2019 19:00, 335716hdjsngrhrs

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

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answered: deanlmartin

(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).

answered: Guest

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

$\frac{2}{5}=\frac{x-18}{x}$

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so:

$\frac{2}{5}=\frac{30-18}{30}$

$\frac{2}{5}=\frac{12}{30}$

$Answer this question! eric has a riddle "i am thinking of a fraction that is equivalent to 2/5 and$

answered: Guest

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1