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JEE Main 201325 AprilOnline
Exam
JEE Main
Year
2013
Date
25 April
Mode
Online
Subject
Mathematics
Chapter
Circle

JEE Main 2013 · 25 April · Online · Mathematics · Circle

Statement 1: The only circle having radius 10 and a diameter along...

Statement 1: The only circle having radius 10\sqrt{10} and a diameter along line 2x+y=52 x+y=5 is x2+y2−6xx^2+y^2-6 x +2y=0+2 y=0. Statement 2:2x+y=52: 2 x+y=5 is a normal to the circle x2+y2−6x+2y=0x^2+y^2-6 x+2 y=0.Statement 1: The only circle having radius 10 and a diameter along line 2 x+y=5 is x^2+y^2-6 x +2 y=0 . Statement 2: 2

Options

  1. AStatement 1 is false; Statement 2 is true.
  2. BStatement 1 is true; Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
  3. CStatement 1 is true; Statement 2 is false.
  4. DStatement 1 is true; Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.

Correct answer

A. Statement 1 is false; Statement 2 is true.

Step-by-step solution

Circle: x2+y2−6x+2y=0x^2+y^2-6 x+2 y=0 Line: 2x+y=52 x+y=5 Centre =(3,−1)=(3,-1) Now, 2×3−1=52 \times 3-1=5, hence centre lies on the given line. Therefore line passes through the centre. The given line is normal to the circle. Thus statement- 2 is true, but statement- 1 is not true as there are infinite circle according to the given conditions. Statement 1: The only circle having radius 10 and a diameter along line 2 x+y=5 is x^2+y^2-6 x +2 y=0 . Statement 2: 2
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