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Question 132267: Choose the correct coordinates of the foci
x2 + 4y2 - 16 = 0
is it (0, -√12) and (0, √12)
or
(0, -2√3) and (0, 2√3)
Answer by nycsharkman(136)   (Show Source):
You can put this solution on YOUR website! Choose the correct coordinates of the foci
x2 + 4y2 - 16 = 0
We are dealing with an ellipse.
The first thing to do is to write this in standard form.
x^2 + 4y^2 - 16 = 0
Add 16 on both sides.
x^2 + 4y^2 = 16
We now divide all three terms by 16 to get 1 on the left side because we want the equation to be in standard form.
x^2/16 + 4y^2/16 = 16/16
x^2/16 + y^2/4 = 1
Since 16 is bigger than 4, the x^2 terms has the BIGGER denominator.
This means our general form for this equation is
x^2/a^2 + y^2/b^2 = 1
The foci is the following sets of points:
(-c, 0) and (c, 0)
To find c, use this:
c^2 = a^2 - b^2
The square root of 16 = 4 = a^2.
The square root of 4 = 2 = b^2
Then:
c^2 = 4 - 2
c^2 = 2
Take square root of both sides:
c = +2, -2
I got the following two points for the foci:
(2, 0) and (-2, 0)
Recheck your work to make sure. Also, reject my work for more practice on your part.
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