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NDA 2017 Maths · Mathematics · Circles · medium

The equation of the circle having the points (1,2) and (5,4) as ends of a diameter is

Single correct option

The equation of the circle having the points (1,2)(1,2) and (5,4)(5,4) as ends of a diameter is
  1. A. x2+y2+6x+6y+13=0x^2+y^2+6x+6y+13=0
  2. B. x2+y2−6x−6y+13=0x^2+y^2-6x-6y+13=0
  3. C. x2+y2−6x−6y−13=0x^2+y^2-6x-6y-13=0
  4. D. x2+y2−6x−6y+3=0x^2+y^2-6x-6y+3=0
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Answer: (B) x2+y2−6x−6y+13=0x^2+y^2-6x-6y+13=0

The diameter form is (x−1)(x−5)+(y−2)(y−4)=0(x-1)(x-5)+(y-2)(y-4)=0, which expands to x2+y2−6x−6y+13=0x^2+y^2-6x-6y+13=0. The wrong options flip a sign or change the constant; checking that (1,2)(1,2) satisfies the equation, 1+4−6−12+13=01+4-6-12+13=0, rejects all three.
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Original question written in the NDA 2017 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