Question

The equation of a directrix of the ellipse \( \frac{x^2}{16} + \frac{y^2}{25} = 1 \) is

• A. \( 3y = 5 \)
• B. \( y = 5 \)
• C. \( 3y = 25 \)
• D. \( y = 5 \)

Hint:

The equation of the directrix of an ellipse is given by \( y = \pm \frac{b^2}{a} \) for standard forms of the ellipse equation.

Answer 1

The Correct Option is C

Step 1: Understanding the equation of ellipse.
The standard equation of an ellipse is \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \), where the directrix is given by \( y = \pm \frac{b^2}{a} \). For the given ellipse, the correct directrix equation is \( 3y = 25 \).

Step 2: Conclusion.
Thus, the correct answer is option (C).

Final Answer: \[ \boxed{\text{(C) } 3y = 25} \]