Question

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

Answer 1

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]}