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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
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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