Aspire Faculty ID #12090 · Topic: CUET 2025 · Just now
CUET 2025

If $x^2 =-16y$ is an equation of parabala 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 latusrectum =16 

Choose the correct answer from the options given below: 

1. (A) and (E) only 
2. (B), (C) and (E) only 
3. (A), (C) and (E) only 
4. (B), (D) and (E) only

Solution

Given \(x^{2}=-16y\). 
Compare with the standard form \(x^{2}=-4ay\) ⇒ \(4a=16\Rightarrow a=4\). 

Hence the parabola opens downward with vertex \((0,0)\), focus \((0,-4)\), directrix \(y=4\), and latus rectum \(=4a=16\). 
Checking options: 
(A) \(y=4\) ✅, 
(B) \(x=4\) ❌, 
(C) \((0,-4)\) ✅, 
(D) \((-4,0)\) ❌, 
(E) \(16\) ✅. 

Therefore, the correct choice is \(\boxed{3\text{ — (A), (C), and (E) only}}\).
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