SOLUTION: I need help with this problem: Identify the conic section whose equation is {{{ x^2 + 4y^2 - 16y = 0}}} and write the equation in standard form. Describe as completely as possibl

Algebra ->  Finance -> SOLUTION: I need help with this problem: Identify the conic section whose equation is {{{ x^2 + 4y^2 - 16y = 0}}} and write the equation in standard form. Describe as completely as possibl      Log On


   

Question 996230: I need help with this problem:
Identify the conic section whose equation is +x%5E2+%2B+4y%5E2+-+16y+=+0 and write the equation in standard form.
Describe as completely as possible the conic section.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
+x%5E2+%2B+4y%5E2+-+16y+=+0

+x%5E2+%2B+4%28y%5E2+-+4y+%29=+0........complete square
+x%5E2%2F4+%2B+%28y%5E2+-+4y%2B2%5E2%29-4=+0
+x%5E2%2F4+%2B+%28y-+2%29%5E2-4=+0
+x%5E2%2F4+%2B+%28y-+2%29%5E2=4....both sides divide by 4
+x%5E2%2F16+%2B+%28y-+2%29%5E2%2F4=+1
+x%5E2%2F16+%2B%28y-+2%29%5E2%2F4=+1.....+x%5E2%2F16 we can write as +%28x-0%29%5E2%2F16

+%28x-0%29%5E2%2F16+%2B%28y-+2%29%5E2%2F4=+1
so, you have an ellipse that has:
h=0,k=2
a=4=>semi-major axis length
b=2=>semi-minor axis length
c%5E2=4%5E2-2%5E2
c%5E2=12
c=sqrt%2812%29
c=2sqrt%283%29
the center is at (0,2)
foci : (c,k), (-c,k)
(2sqrt%283%29, 2)
(-2sqrt%283%29, 2)
vertices: (a, k), (4-a, k)
(4, 2)
(-4, 2)
eccentricity : c%2Fa=2sqrt%283%29%2F4=sqrt%283%29%2F2