Question 1146431
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NB: Use ^ (shift-6) to denote exponentiation -- e.g., 9x^2 instead of 9x2.<br>
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:<br>
a. {{{9x^2 + 25y^2 - 225 = 0}}} ​--> {{{x^2/5^2+y^2/3^2 = 1}}} --> horizontal half axis 5, vertical 3 --> possible answer<br>​ ​
b. {{{16x^2 + 25y^2 - 400 = 0}}} ​--> {{{x^2/5^2+y^2/4^2 = 1}}} --> horizontal half axis 5, vertical 4 --> possible answer<br>​
​c. {{{25x^2 + 9y^2 - 225 = 0}}} ​--> {{{x^2/3^2+y^2/5^2 = 1}}} --> horizontal half axis 3, vertical 5 --> NOT a possible answer<br>​
​d. {{{25x^2 + 16y^2 - 400 = 0}}} ​--> {{{x^2/4^2+y^2/5^2 = 1}}} --> horizontal half axis 4, vertical 5 --> NOT a possible answer<br>​
So the answer is either a or b....<br>
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,<br>
a=5, b=3 --> circumference 25.53
a=5, b=4 --> circumference 28.36<br>
The stated circumference is 28.448.  That makes choice b the best choice....