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NDA 2018 Maths · Mathematics · Straight Lines · medium

The equation of the circle of radius 5 that touches both coordinate axes and lies in the first quadrant is

Single correct option

The equation of the circle of radius 5 that touches both coordinate axes and lies in the first quadrant is
  1. A. x2+y2−10x−10y+25=0x^2+y^2-10x-10y+25=0
  2. B. x2+y2−5x−5y+25=0x^2+y^2-5x-5y+25=0
  3. C. x2+y2+10x+10y+25=0x^2+y^2+10x+10y+25=0
  4. D. x2+y2−10x−10y=0x^2+y^2-10x-10y=0
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Answer: (A) x2+y2−10x−10y+25=0x^2+y^2-10x-10y+25=0

A circle touching both axes in the first quadrant has centre (5,5)(5,5) for radius 5. So (x−5)2+(y−5)2=25(x-5)^2+(y-5)^2=25, which expands to x2+y2−10x−10y+25=0x^2+y^2-10x-10y+25=0. The last option passes through the origin, so it cuts the axes instead of touching them.
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Original question written in the NDA 2018 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