JEE Main Coordinate Geometry: Conic Sections – Chapter Test

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Difficulty: 10 medium · 10 hard

Conic Sections MCQ questions with answers

The first 3 of 20 questions. Unlock the series for the rest, each with a solution.

1. Q1. The length of the latus rectum of the hyperbola x²/9 − y²/16 = 1 is:

   अतिपरवलय x²/9 − y²/16 = 1 के नाभिलंब जीवा (latus rectum) की लंबाई है:

   • A. 16/3
   • B. 9/4
   • C. 8/3
   • D. 32/3
   Solution

   For x²/a² − y²/b² = 1 the latus rectum is 2b²/a. Here a = 3, b² = 16, so it equals 2·16/3 = 32/3.

   x²/a² − y²/b² = 1 के लिए नाभिलंब जीवा 2b²/a होती है। यहाँ a = 3, b² = 16, अतः यह 2·16/3 = 32/3 के बराबर है।

2. Q2. For the ellipse x²/a² + y²/b² = 1 with a > b, the length of the latus rectum is:

   दीर्घवृत्त x²/a² + y²/b² = 1 (जहाँ a > b) के लिए, नाभिलंब जीवा की लंबाई है:

   • A. a²/b
   • B. b²/2a
   • C. 2b²/a
   • D. 2a²/b
   Solution

   The latus rectum of such an ellipse is 2b²/a.

   ऐसे दीर्घवृत्त की नाभिलंब जीवा 2b²/a होती है।

3. Q3. The distance between the two foci of the ellipse x²/25 + y²/16 = 1 is:

   दीर्घवृत्त x²/25 + y²/16 = 1 की दोनों नाभियों के बीच की दूरी है:

   • A. 8
   • B. 10
   • C. 6
   • D. 3
   Solution

   Here a = 5 and e = √(1 − 16/25) = 3/5, so the distance between the foci is 2ae = 2·5·(3/5) = 6.

   यहाँ a = 5 और e = √(1 − 16/25) = 3/5, अतः नाभियों के बीच की दूरी 2ae = 2·5·(3/5) = 6 है।

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