Question

If \( x^2 = -16y \) is an equation of a parabola, then: 

(A) Directrix is \( y = 4 \) 
(B) Directrix is \( x = 4 \) 
(C) Co-ordinates of focus are \( (0, -4) \) 
(D) Co-ordinates of focus are \( (-4, 0) \) 
(E) Length of latus rectum is 16 
 

• A. (A) and (E) only
• B. (B), (C) and (E) only
• C. (A), (C) and (E) only
• D. (B), (D) and (E) only

Hint:

For parabolas in the form \( x^2 = -4ay \), the focus is at \( (0, -a) \), the directrix is \( y = a \), and the length of the latus rectum is \( 4a \).

Answer 1

The Correct Option is C

Step 1: Standard form of the parabola.
The given equation \( x^2 = -16y \) is a parabola that opens downwards. The standard form for a parabola opening downwards is: \[ x^2 = -4ay \] By comparing, we see that \( 4a = 16 \), so \( a = 4 \).

Step 2: Find the focus and directrix.
- The focus is at \( (0, -a) = (0, -4) \). - The directrix is given by \( y = a = 4 \).

Step 3: Find the length of the latus rectum.
The length of the latus rectum for a parabola is \( 4a \), which is \( 16 \). Thus, the correct answer is 3. (A), (C) and (E) only.