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:
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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