SOLUTION: Consider the elipse 9x^2+36y^2=324 Which of the following statements about the foci and eccentricity is correct? Only one answer is correct. Which one is correct? A) the foc

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Question 1199124: Consider the elipse 9x^2+36y^2=324
Which of the following statements about the foci and eccentricity is correct?
Only one answer is correct. Which one is correct?
A) the foci are [0,-3(square root of 3)] and [0, 3(square root of 3)], the eccentricity is 1/2(square root of 3)
B) the foci are [0,-3(square root of 3)] and [0, 3(square root of 3)], the eccentricity is square root of 3
C) the foci are [(-3(square root of 3), 0] and [3(square root of 3),0)], the eccentricity is 1/2(square root of 3)
D) the foci are [(-3(square root of 3),0] and [3(square root of 3),0], the eccentricity is square root of 3


Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

9x%5E2%2B36y%5E2=324
9x%5E2%2F324%2B36y%5E2%2F324=324%2F324
x%5E2%2F36%2By%5E2%2F9=1
so
center at (0, 0), =>h=0,k=0
a=6
b=3
c=sqrt%286%5E2-3%5E2%29=sqrt%2827%29=3sqrt%283%29
since a focus is at (h-c, k)=>a foci are at (3sqrt%283%29,0) and (-3sqrt%283%29,0)
eccentricity
e=c%2Fa=3sqrt%283%29%2F6=%281%2F2%29sqrt%283%29

answer:
C)