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

Jun 8, 2015

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

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

${y}^{2} = 4 \left(9 - {x}^{2}\right) = 36 - 4 {x}^{2}$

Then add $4 {x}^{2}$ to both sides to get:

$4 {x}^{2} + {y}^{2} = 36$

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

$a {x}^{2} + b {y}^{2} = c$, 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]}