SOLUTION: The perimeter of an ellipse is 28.448 units. Its major axis is 10 units long and is horizontal. If its center is at the origin, find the equation of the ellipse. a. 9x2 + 25y2 -

Question 1146431: The perimeter of an ellipse is 28.448 units. Its major axis is 10 units long and is horizontal. If its center is at the origin, find the equation of the ellipse.
a. 9x2 + 25y2 - 225 = 0
b. 16x2 + 25y2 - 400 = 0
c. 25x2 + 9y2 - 225 = 0
d. 25x2 + 16y2 - 400 = 0
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

NB: Use ^ (shift-6) to denote exponentiation -- e.g., 9x^2 instead of 9x2.

Major axis length 10 and horizontal means the semi-major axis is 5 in the x direction. That makes only two of the answer choices possible correct answers:

a. --> --> horizontal half axis 5, vertical 3 --> possible answer

b. --> --> horizontal half axis 5, vertical 4 --> possible answer

c. --> --> horizontal half axis 3, vertical 5 --> NOT a possible answer

d. --> --> horizontal half axis 4, vertical 5 --> NOT a possible answer

So the answer is either a or b....

There are online calculators for finding the (approximate) circumference of an ellipse from the values of a and b. Using one of them, I find, using the two possible answers above,

a=5, b=3 --> circumference 25.53
a=5, b=4 --> circumference 28.36

The stated circumference is 28.448. That makes choice b the best choice....
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