Question

Help with ellipses

Answer 1

Find the equation of the following an ellipse based on the following information: Foci: (0, 0), (0, 8), Major axis of length 16, and a minor axis of length 4.

Answer 2

so you can find a and b by dividing 16/2 and 4/2 which:

a=8 b=2

Answer 3

so our equation would look like;

\[\frac{ (x-h)^2 }{ 8^2 }-\frac{ (y-h)^2 }{ 2^2 }=1\]

Answer 4

ok, but the focuses lie on the major axis

Answer 5

Would that affect a and b?

Answer 6

1) the center will be at the mid-point between the two foci (so find the average of the two).
2) you add the two terms (you show subtraction... I think that is a hyperbola)
3) the major axis lies on the y axis (because foci (0,0) and (0,8) lie on the y axis)
that means the "a" goes with the y term

Answer 7

oh I screwed up the equation T_T. It is a plus

Answer 8

the mid point would be 4 and y = 8 as well ?

Answer 9

if you plot (0,0) and (0,8) where is the mid point?
by counting you can see (0,4)
that is the center (h,k). i.e. use h=0 and k=4 in your equation

Answer 10

Oops i meant (0,4) not just 4 sorry.

Answer 11

\[\frac{ x^2 }{ 8^2 }+\frac{ (y-4)^2 }{ 2^2 }=1\]

Answer 12

@phi does this look correct?

Answer 13

except the 8^2 goes with the y (because the major axis is on the y-axis, and the major axis is always the bigger number)