alg
posted by jerson .
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

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?

sorry the problem is 4x^2 + 7y^2 + 32x56y +148=0

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^28y+16 = 4
(4/7)(x+4)^2 + (y4)^2 = 4
(x+4)^2 /7 + (y4)^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(74) = sqrt 3
etc