### Instruction: Compute the area of the ellipse $9x^2 + y^2 = 36.$.### Response: To find the area of the ellipse, I need to know its major and minor axes.
I can rewrite the equation of the ellipse in standard form by dividing both sides by 36: $\frac{x^2}{4} + \frac{y^2}{36} = 1.$
Now I can see that the semi-major axis is $b = 6$ and the semi-minor axis is $a = 2.$
The area of an ellipse is given by the formula $A = \pi ab.$
Plugging in the values of $a$ and $b$, I get $A = \pi \cdot 2 \cdot 6 = 12 \pi.$