Explanation
1. Standard Form se Comparison
Di gayi equation x2=−16y niche di gayi standard form se match karti hai:
Yeh ek downward opening parabola hai (jo niche ki taraf khulta hai).
Donon equations ko compare karne par:
2. Parabola ki Properties Check Karna
Humein a=4 mil gaya hai, ab har option ko check karte hain:
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(C) Co-ordinates of Focus:
Downward parabola (x2=−4ay) ka focus y-axis par hota hai: (0,−a).
Focus =(0,−4).
Yeh TRUE hai.
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(A) Directrix ki Equation:
Iska directrix x-axis ke parallel aur focus ke opposite side hota hai: y=a.
Directrix: y=4.
Yeh TRUE hai.
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(E) Length of Latus Rectum:
Latus rectum ki length hamesha ∣4a∣ hoti hai.
Length =4×4=16.
Yeh TRUE hai.
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(B) aur (D):
(B) mein x=4 diya hai jo galat hai (yeh vertical line hai). (D) mein focus (−4,0) diya hai jo x-axis par hai, isliye galat hai.
Final Answer
Sahi statements hain: (A), (C), aur (E).
