SOLUTION: I need to find the foci, vertices, directrix, axis for 4(x-1)^2+y^2=1

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Question 397055: I need to find the foci, vertices, directrix, axis for 4(x-1)^2+y^2=1
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
4%28x-1%29%5E2%2By%5E2=1<==> %28x-1%29%5E2%2F%281%2F4%29%2By%5E2%2F1=1
The conic section is an ellipse.
The center of the ellipse is (1,0).
The major axis x = 1, the minor axis y = 0.
Here, a%5E2+=+1, and b%5E2+=+1%2F4, and so b%5E2+=+a%5E2+-+c%5E2, or
1%2F4+=+1+-+c%5E2, or c%5E2+=+3%2F4, or c = sqrt%283%29%2F2.
Therefore the foci are (1, sqrt%283%29%2F2) and (1, -sqrt%283%29%2F2).
The vertices are (1, 1) and (1, -1). The co-vertices are (1/2, 0) and (3/2, 0).
The eccentricity is e+=+c%2Fa+=++sqrt%283%29%2F2
==> The directrices are y+=+a%2Fe+=+2%2Fsqrt%283%29 and y+=+-a%2Fe+=+-2%2Fsqrt%283%29