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JEE Main 2022 · Mathematics · Straight Lines and Circles · easy

The radius of the circle passing through the points (0,0), (4,0) and (0,6) is

Single correct option

The radius of the circle passing through the points (0,0)(0,0), (4,0)(4,0) and (0,6)(0,6) is
  1. A. 55
  2. B. 1313
  3. C. 13\sqrt{13}
  4. D. 2132\sqrt{13}
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Answer: (C) 13\sqrt{13}

The points (0,0),(4,0),(0,6)(0,0),(4,0),(0,6) form a right angle at the origin, so the hypotenuse joining (4,0)(4,0) and (0,6)(0,6) is a diameter. Its length is 16+36=213\sqrt{16+36}=2\sqrt{13}, hence the radius is 13\sqrt{13}. Equivalently the circle is x2+y2−4x−6y=0x^2+y^2-4x-6y=0 with r2=4+9=13r^2=4+9=13.
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Original question written in the JEE Main 2022 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake