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NDA 2024 Maths · Mathematics · Circles · medium

The equation of the circle concentric with x^2+y^2-4x+2y-7=0 and passing through the point (1,1) is

Single correct option

The equation of the circle concentric with x2+y2−4x+2y−7=0x^2+y^2-4x+2y-7=0 and passing through the point (1,1)(1,1) is
  1. A. x2+y2−4x+2y−7=0x^2+y^2-4x+2y-7=0
  2. B. x2+y2−4x+2y+5=0x^2+y^2-4x+2y+5=0
  3. C. x2+y2−4x+2y=0x^2+y^2-4x+2y=0
  4. D. x2+y2+4x−2y=0x^2+y^2+4x-2y=0
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Answer: (C) x2+y2−4x+2y=0x^2+y^2-4x+2y=0

The centre of the given circle is (2,−1)(2,-1). Distance to (1,1)(1,1) is 1+4=5\sqrt{1+4}=\sqrt5, so the new circle is (x−2)2+(y+1)2=5(x-2)^2+(y+1)^2=5, i.e. x2+y2−4x+2y=0x^2+y^2-4x+2y=0. Trap: the given circle itself is the second option (it does not pass through (1,1)(1,1): 1+1−4+2−7≠01+1-4+2-7\ne0), and the last option flips the centre.
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