SOLUTION: Write the equation in standard form for an ellipse centered at (h,k). Identify the center and the vertices. 4x^2 + 8x + y^2 + 2y + 1 = 0

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Write the equation in standard form for an ellipse centered at (h,k). Identify the center and the vertices. 4x^2 + 8x + y^2 + 2y + 1 = 0      Log On


   

Question 444286: Write the equation in standard form for an ellipse centered at (h,k). Identify the center and the vertices.
4x^2 + 8x + y^2 + 2y + 1 = 0
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi



Standard Form of an Equation of an Ellipse is %28x-h%29%5E2%2Fa%5E2+%2B+%28y-k%29%5E2%2Fb%5E2+=+1+

where Pt(h,k) is the center and a and b  are the respective vertices distances from center.

 4x^2 + 8x + y^2 + 2y + 1 = 0  

4(x+1)^2 -4 + (y+1)^2 -1 +1 = 0

4(x+1)^2 + (y+1)^2 = 4

+%28x%2B1%29%5E2%2F1+%2B+%28y%2B1%29%5E2%2F4+=+1  sqrt(4-1) = sqrt(3) = 1.732

 Center (-1,-1) foci (-1, -2.732) and (-1,.732)