Maths · Coordinate geometry · chapter 10 of 14
Class 11 Maths Chapter 10: Conic Sections Assertion-reason questions with answers
2 assertion-reason questions on Conic Sections, each with its answer and the reason, written from the NCERT chapter. For school exams on the CBSE pattern and JEE Main, which are set from the same NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter. Each question gives an Assertion (A) and a Reason (R); choose how they stand to each other.
Question 1
Assertion (A): The ellipses x216 + y27 = 1 and x232 + y214 = 1 have the same eccentricity. Reason (R): The eccentricity of the ellipse x2a2 + y2b2 = 1 (a > b) is √(1 − b2a2), which depends only on the ratio b2a2.
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Answer: (a) Both A and R are true, and R is the correct explanation of A.
e = ca with c2 = a2 − b2 gives e = √(1 − b2a2): R is true. Both ellipses have b2a2 = 716, so both have e = 34: A is true, and R is why.
Question 2
Assertion (A): The set of points of the plane equidistant from the point (2, 0) and the line x = 2 is the line x = 2. Reason (R): If the fixed point lies on the fixed line, the set of points equidistant from them is the line through the fixed point perpendicular to the fixed line.
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Answer: (d) A is false, but R is true.
R is NCERT's degenerate case of the parabola. The point (2, 0) lies on x = 2, so the locus is the line through (2, 0) perpendicular to x = 2, which is y = 0, not x = 2. A is false, R is true.
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