How do you graph y=2sqrt(9-x^2)?

1 Answer
George C.
Jun 8, 2015

This is the upper half of an ellipse with endpoints on the x axis at (-3, 0) and (3, 0), reaching its maximum value where it cuts the y axis at (0, 6)

To see this, first square both sides of the equation to get:

y^2=4(9-x^2) = 36 - 4x^2

Then add 4x^2 to both sides to get:

4x^2+y^2=36

This is in the general form of the equation of an ellipse:

ax^2 + by^2 = c, where a, b, c > 0

However, the square root sign denotes the positive square root, so the original equation only represents the upper half of the ellipse.

graph{2sqrt(9-x^2) [-10.085, 9.915, -2, 8]}

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