SOLUTION: Find the vertices, the endpoints of the minor axis, and the foci of the ellipse {{{4x^2+16x+y^2+2y+1=0}}}. I dont even know where to begin on this problem, I would really apprec

Question 113835: Find the vertices, the endpoints of the minor axis, and the foci of the ellipse .
I dont even know where to begin on this problem, I would really appreciate it if someone could help me. Thank you!!!
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
the general equation for this ellipse is

this is an ellipse with a semimajor axis a and semiminor axis b, centered at the point (h,k)

if c is the distance from the center to a focus, then c^2=a^2-b^2

___ ___

dividing by 16 gives

the center (-2,-1) is midway between the foci
___ a=4; is the distance from center to vertex
___ b=2, so c^2=(4^2-2^2) ___ c^2=12

vertices ___ (-2,3) and (-2,-5)
minor axis endpoints ___ (-4,-1)(0,-1)
foci ___ (-2,(sqrt(12)-1)) and (-2,-((sqrt(12))+1))
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