1. **Stating the problem:** We are given the equation $$9x^2 + 4y^2 = 36$$ and asked to identify which of the given options matches this equation when rewritten in the standard form of an ellipse. 2. **Formula and rules:** The standard form of an ellipse centered at the origin with axes aligned to coordinate axes is $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$$ where $a^2$ and $b^2$ are the denominators under $x^2$ and $y^2$ respectively. 3. **Rewrite the given equation:** Divide both sides of the equation by 36 to get 1 on the right side: $$\frac{9x^2}{36} + \frac{4y^2}{36} = \frac{36}{36}$$ Simplify the fractions: $$\frac{x^2}{4} + \frac{y^2}{9} = 1$$ 4. **Compare with options:** - a. $$\frac{x^2}{16} + \frac{y^2}{9} = 1$$ (denominator under $x^2$ is 16, not 4) - b. $$\frac{x^2}{4} + \frac{y^2}{9} = 1$$ (matches exactly) - c. $$\frac{x^2}{25} + \frac{y^2}{4} = 1$$ (does not match) - d. $$\frac{x^2}{9} + \frac{y^2}{1} = 1$$ (does not match) 5. **Conclusion:** The correct equation in standard form is option b. 6. **Graph description:** This ellipse is centered at the origin $(0,0)$ with semi-major axis $b = 3$ along the y-axis and semi-minor axis $a = 2$ along the x-axis. **Final answer:** b. $$\frac{x^2}{4} + \frac{y^2}{9} = 1$$