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NDA 1 2024 Maths, question 51

Topic: Analytical geometry

Q51

If (a,b)(a,b) is the centre and cc is the radius of the circle x2+y2+2x+6y+1=0x^{2}+y^{2}+2x+6y+1=0, then what is the value of a2+b2+c2a^{2}+b^{2}+c^{2} ?

  1. (a) 1919Correct answer
  2. (b) 1818
  3. (c) 1717
  4. (d) 1111

Solution.

Answer: (a) 1919

  1. Complete squares to obtain centre (−1, −3) and radius 3.
  2. The requested sum is (−1)² + (−3)² + 3² = 19.