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NDA 2020 Maths · Mathematics · Circles · hard

The circle passing through the origin and the points (4,0) and (0,6) has radius

Single correct option

The circle passing through the origin and the points (4,0)(4,0) and (0,6)(0,6) has radius
  1. A. 1313
  2. B. 2132\sqrt{13}
  3. C. 55
  4. D. 13\sqrt{13}
Show answer and solution

Answer: (D) 13\sqrt{13}

A circle through the origin is x2+y2+2gx+2fy=0x^2+y^2+2gx+2fy=0. Using (4,0)(4,0): 16+8g=016+8g=0, so g=−2g=-2. Using (0,6)(0,6): 36+12f=036+12f=0, so f=−3f=-3. Radius =g2+f2=13=\sqrt{g^2+f^2}=\sqrt{13}. The value 2132\sqrt{13} is the diameter, which equals the hypotenuse of the right triangle with legs 44 and 66, and 1313 is the square of the radius.
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Original question written in the NDA 2020 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake