SOLUTION: what are 2 functions for the following equation: ((x+1)/10)^2 + (y/5)^2 = 1

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Question 111547: what are 2 functions for the following equation:
((x+1)/10)^2 + (y/5)^2 = 1
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
what are 2 functions for the following equation:
%28%28x%2B1%29%2F10%29%5E2+%2B+%28y%2F5%29%5E2+=+1

This is the equation of this ellipse:



An ellipse is NOT a function because it does not pass the
vertical line test.

However the upper half of the ellipse is a function:



Also the lower half of the ellipse is a function:



To find these two functions we solve the equation for y:

%28%28x%2B1%29%2F10%29%5E2+%2B+%28y%2F5%29%5E2+=+1
%28x%2B1%29%5E2%2F10%5E2+%2B+y%5E2%2F5%5E2+=+1
%28x%2B1%29%5E2%2F100+%2B+y%5E2%2F25+=+1
Multiply through by LCD = 100
%28x%2B1%29%5E2+%2B+4y%5E2+=+100
4y%5E2+=+100-%28x%2B1%29%5E2
4y%5E2+=+100-%28x%5E2%2B2x%2B1%29
4y%5E2+=+100-x%5E2-2x-1
4y%5E2+=+99-x%5E2-2x
y%5E2+=+%2899-x%5E2-2x%29%2F4
y = ±sqrt%2899-x%5E2-2x%29%2F2

When we use the positive sign we get the
functional equation

y = sqrt%2899-x%5E2-2x%29%2F2

which is the equation of the top half of
the ellipse.

When we use the negative sign we get the
functional equation

y = -sqrt%2899-x%5E2-2x%29%2F2

which is the equation of the bottom half of
the ellipse.

Edwin