Given the equation 2x^2 - 50y^2 = 50 determine:

a) The Center C

b) The 2 Vertices

c) The slopes of the asymptotes

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The given equation is `2x^2 - 50y^2 = 50`

Divide both sides by 50:

`x^2/25-y^2/1=1`

`rArr(x-0)^2/5^2-(y-0)^2/1^2=1`

This is the equation of a hyperbola with horizontal transverse axis.

Its standard form is `(x-h)^2/a^2-(y-k)^2/b^2=1` where `(h,k)` is its center.

a) **The Center C =(h,k) =(0,0).**

b) To find the two vertices of the given hyperbola apply the formula `(h+a,k)` and `(h-a,k).`

Here, h=k=0 and a=5

**Hence, the two vertices are (5,0) and (-5,0).**

c) To find the slopes of the asymptotes of the hyperbola with horizontal transverse axis apply the formula `m=+-b/a.`

Here, a=5, b=1

**Hence, the slopes of the asymptotes of the given hyperbola are **`m=+-1/5.`

**Sources:**

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