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NDA 2020 Maths · Mathematics · Circles · easy

The equation of the circle with centre (-2,3) that touches the x-axis is

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The equation of the circle with centre (−2,3)(-2,3) that touches the x-axis is
  1. A. (x+2)2+(y−3)2=4(x+2)^2+(y-3)^2=4
  2. B. (x−2)2+(y+3)2=9(x-2)^2+(y+3)^2=9
  3. C. (x+2)2+(y−3)2=13(x+2)^2+(y-3)^2=13
  4. D. (x+2)2+(y−3)2=9(x+2)^2+(y-3)^2=9
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Answer: (D) (x+2)2+(y−3)2=9(x+2)^2+(y-3)^2=9

A circle touching the x-axis has radius equal to the absolute value of the y-coordinate of its centre, so r=3r=3. Hence the circle is (x+2)2+(y−3)2=9(x+2)^2+(y-3)^2=9. The option with 44 uses the x-coordinate's magnitude as the radius (that would touch the y-axis), 1313 is the squared distance of the centre from the origin, and the option with signs reversed has centre (2,−3)(2,-3).
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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