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
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
Show Hint
- (A) and (E) only
- (B), (C) and (E) only
- (A), (C) and (E) only
- (B), (D) and (E) only
The Correct Option is C
Solution and Explanation
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.
Top Questions on Parabola
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