SOLUTION: I need help with this too, Please: Find the vertices, the endpoints of the minor axis, and foci of the given ellipse, and sketch it's graph: 4x squared + y squared

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Question 35469This question is from textbook algebra for college students
: I need help with this too, Please:
Find the vertices, the endpoints of the minor axis, and foci of the given ellipse, and sketch it's graph:
4x squared + y squared - 8y + 4y + 4 = 0 This question is from textbook algebra for college students

Answer by Nate(3500) (Show Source):
You can put this solution on YOUR website!
4x^2 + y^2 - 8y + 4y + 4 = 0
4x^2 - 8x + y^2 + 4y = -4
4(x^2 - 2x) + (y^2 + 4y) = -4
4(x - 1)^2 + (y + 2)^2 = 4
((x - 1)^2) + ((y + 2)^2)/4 = 1
center (1,-2)
has a vertical major axis
a(length of major axis) = 2
b(length of minor axis) = 1
c^2 = a^2 - b^2
c^2 = 4 - 1
c = 3^(1/2) or -3^(1/2) length cannot be negative so the c is 3^(1/2)
foci: (1+3^(1/2),-2) and (1-3^(1/2),-2)

SOLUTION: I need help with this too, Please: Find the vertices, the endpoints of the minor axis, and foci of the given ellipse, and sketch it's graph: 4x squared + y squared - 8y + 4y