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algebra

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Find the vertices and foci of this ellipse 4x^2+16y^2+64x+64y+256=0

  • algebra - ,

    4x^2+16y^2+64x+64y+256=0
    4x^2+64x+256 + 16y^2+64y+64 = -256
    4(x+8)^2 + 16(y+2)^2 = -256 + 256 + 64
    (x+8)^2 + 4(y+2)^2 = 16

    (x+8)^2/16 + (y+2)^2/4 = 1

    h=-8 k=-2
    a=4 b=2 c=√12

    center: (-8,-2)
    vertices: (-12,-2) (-4,-2)
    foci: (-8-√12,-2) (-8+√12,-2)

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