SOLUTION: Give the equation X^2+4y^2=16 find: a. The center C (use (,)) b. Length of major axis c. Length of minor axis d. Distance from C to foci c hint: divide by 16

Algebra ->  Finance -> SOLUTION: Give the equation X^2+4y^2=16 find: a. The center C (use (,)) b. Length of major axis c. Length of minor axis d. Distance from C to foci c hint: divide by 16      Log On


   

Question 1118319: Give the equation
X^2+4y^2=16 find:
a. The center C (use (,))
b. Length of major axis
c. Length of minor axis
d. Distance from C to foci c
hint: divide by 16
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


x%5E2%2B4y%5E2+=+16
x%5E2%2F16+%2B+y%5E2%2F4+=+1
x%5E2%2F4%5E2+%2B+y%5E2%2F2%5E2+=+1
%28x-0%29%5E2%2F4%5E2+%2B+%28y-0%29%5E2%2F2%5E2+=+1
%28x-h%29%5E2%2Fa%5E2+%2B+%28y-k%29%5E2%2Fb%5E2+=+1

The "x-0" and "y-0" mean the center of the ellipse is (h,k) = (0,0).

a. Answer: the center is C(0,0).

The denominators are the squares of the semi-major and semi-minor axes. So the semi-major axis is 4 (in the x direction) and the semi-minor axis is 2 (in the y direction). So the lengths of the major and minor axes are 8 and 4.

b,c. Answer: major axis 8; minor axis 4.

"c" is the distance from the center of the ellipse to either focus; for an ellipse, c^2 = a^2 + b^2.

d. Answer: the distance from the center to each focus is sqrt%2816%2B4%29+=+sqrt%2820%29