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Given the equation 2x^2 - 50y^2 = 50 determine: a) The Center C b) The 2 Vertices c)...

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kristenmarieb... | Student, Grade 10 | Valedictorian

Posted July 19, 2013 at 2:45 AM via web

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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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llltkl | College Teacher | Valedictorian

Posted July 19, 2013 at 3:43 AM (Answer #1)

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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.`

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