SOLUTION: Give the equation 4x^2+9y^2=36 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 36 How do y

Algebra ->  Finance -> SOLUTION: Give the equation 4x^2+9y^2=36 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 36 How do y      Log On


   

Question 1118335: Give the equation
4x^2+9y^2=36 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 36
How do you find the distance from C to foci C?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
4x%5E2%2B9y%5E2=36

%284x%5E2%2B9y%5E2%29%2F36=1

x%5E2%2F9%2By%5E2%2F4=1

note the relationship x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2=1, and there is a constant c so that c%5E2=a%5E2-b%5E2.
Your example has c%5E2=9-4=5
and from that,
c=sqrt%285%29.

Your foci each is c=sqrt(5) from the center of the ellipse and are along the long axis of the ellipse.

Major axis is horizontal, along the x-axis.

You have %28x-0%29%5E2%2F9%2B%28y-0%29%5E2%2F4=1 so the center point is at (0,0).
Foci are at ( -sqrt%285%29, 0 ) and (sqrt%285%29, 0 ).