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JEE Main 2019 · Mathematics · Straight Lines and Circles · hard

A circle passes through the origin and cuts off intercepts of lengths 4 and 6 on the positive x-axis and positive y-axis respectively. Its radius is

Single correct option

A circle passes through the origin and cuts off intercepts of lengths 4 and 6 on the positive xx-axis and positive yy-axis respectively. Its radius is
  1. A. 13\sqrt{13}
  2. B. 52\sqrt{52}
  3. C. 5
  4. D. 26\sqrt{26}
Show answer and solution

Answer: (A) 13\sqrt{13}

The circle passes through (0,0),(4,0),(0,6)(0,0),(4,0),(0,6): x2+y2−4x−6y=0x^2+y^2-4x-6y=0. Centre (2,3)(2,3), radius =4+9=13=\sqrt{4+9}=\sqrt{13}. (The right angle at the origin makes the chord joining the intercept points a diameter of length 52\sqrt{52}.)
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