SOLUTION: My question is: Write the equation for the ellipse whose center is the origin, has a horizontal major axis length of 12 and passses through the point (-4,2). I need help with thi

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Question 147808: My question is: Write the equation for the ellipse whose center is the origin, has a horizontal major axis length of 12 and passses through the point (-4,2).
I need help with this, since the horizontal axis is at the origin I get that the foci is (-6,0) and (6,0). I find that the equation will be %28x%5E2%2F36%29%2B%28y%5E2%2Fb%5E2%29=1 but I am having trouble finding what b%5E2 equals. Can you help me?
Found 2 solutions by scott8148, Edwin McCravy:
Answer by scott8148(5896) About Me  (Show Source):
You can put this solution on YOUR website!
substituting the coordinates of the point __ (16/36)+(4/(b^2))=1

subtracting 16/36 __ 4/(b^2)=20/36 __ "cross" multiplying __ 144=20b^2

dividing by 20 __ 36/5=b^2

Answer by Edwin McCravy(6941) About Me  (Show Source):
You can put this solution on YOUR website!
SOLUTION BY EDWIN
My question is: Write the equation for the ellipse whose center is the origin, has a horizontal major axis length of 12 and passses through the point (-4,2).
I need help with this, since the horizontal axis is at the origin I get that the foci is (-6,0) and (6,0). I find that the equation will be %28x%5E2%2F36%29%2B%28y%5E2%2Fb%5E2%29=1 but I am having trouble finding what b%5E2 equals. Can you help me?
Go back and look at the problem to see what if anything you haven't used. Here's what you haven't used:
>>...passses through the point (-4,2)...<<
So you see that all you need do is plug the point (-4,2) into
%28x%5E2%2F36%29%2B%28y%5E2%2Fb%5E2%29=1 and solve for b.
%28x%5E2%2F36%29%2B%28y%5E2%2Fb%5E2%29=1
%28%28-4%29%5E2%2F36%29%2B%28%282%29%5E2%2Fb%5E2%29=1
16%2F36%2B4%2Fb%5E2=1
4%2F9%2B4%2Fb%5E2=1
Clear of fractions by multiplying thru by 9b%5E2
9b%5E2%2A4%2F9%2B9b%5E2%2A4%2Fb%5E2=9b%5E2%2A1

cross%289%29b%5E2%2A4%2Fcross%289%29%2B9cross%28b%5E2%29%2A4%2Fcross%28b%5E2%29=9b%5E2
4b%5E2%2B36=9b%5E2
36=5b%5E2
36%2F5=b%5E2
That's an ugly answer, but it is correct. So
the equation of the ellipse in standard form is
x%5E2%2F36%2By%5E2%2F%2836%2F5%29=1

Here is its graph:
drawing%28400%2C400%2C-10%2C10%2C-10%2C10%2C+grid%281%29%2C+locate%28-4-.2%2C2.4%2C%27@%27%29%2C+graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Csqrt%28%2836-x%5E2%29%2F5%29%29%2C+locate%28-6.4-.2%2C2.7%2C%27%28-4%2C2%29%27%29%2C+%0D%0Agraph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-sqrt%28%2836-x%5E2%29%2F5%29%29%0D%0A+%0D%0A%29
But if you don't necessarily have to have it in standard
form, you can simplify it.
x%5E2%2F36%2By%5E2%2F%2836%2F5%29=1
Multiply top and bottom of the second fraction by 5
x%5E2%2F36%2B5y%5E2%2F%285%2A%2836%2F5%29%29=1
x%5E2%2F36%2B5y%5E2%2F%28cross%285%29%2A%2836%2Fcross%285%29%29%29=1
x%5E2%2F36%2B5y%5E2%2F36=1
Then multiply through by 36
x%5E2%2B5y%5E2=36

Edwin