1. **State the problem:** We need to write the equation of the ellipse given by $$9x^2 + 4y^2 = 36$$ in standard form. 2. **Recall the standard form of an ellipse:** The standard form is $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$ where $a^2$ and $b^2$ are the denominators representing the squares of the semi-major and semi-minor axes. 3. **Rewrite the given equation:** Divide both sides of the equation by 36 to get the right side equal to 1: $$\frac{9x^2}{36} + \frac{4y^2}{36} = \frac{36}{36}$$ 4. **Simplify the fractions:** $$\frac{x^2}{4} + \frac{y^2}{9} = 1$$ 5. **Interpret the result:** This matches the form $$\frac{x^2}{4} + \frac{y^2}{9} = 1$$ which corresponds to option b. **Final answer:** b. $$\frac{x^2}{4} + \frac{y^2}{9} = 1$$