identify the conic section. if its a parabols give the vertex if its a circle, give the center and radius. if it is an ellipse or a hyperbola, give the center and foci.
again my teacher said the answer is ellipse with center (-4,4), foci at (-4± V3, 4) but don't get how she got it

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  1. You have not given us the problem that we are supposed to solve. I can not even reverse engineer it from what you have written. What conic section?

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  2. sorry the problem is 4x^2 + 7y^2 + 32x-56y +148=0

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  3. 4 x^2 + 32 x + 7 y^2 -56 y = -148

    x^2 + 8 x + (7/4)y^2 - 14 y = -37
    x^2 + 8 x + 16 + (7/4) y^2 -14 y = -21
    (x+4)^2 + (7/4) y^2 - 14 y = -21
    (4/7)(x+4)^2 + y^2 - 8 y = -12
    (4/7)(x+4)^2 + y^2-8y+16 = 4
    (4/7)(x+4)^2 + (y-4)^2 = 4
    (x+4)^2 /7 + (y-4)^2/4 = 1
    ellipse with center at (-4,4)
    a^2 = 7
    b^2 4
    so a = sqrt 7
    b = 2
    center to focus = sqrt(7-4) = sqrt 3

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