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KCET2011MathematicsApplication of Derivatives

If 2 x²+2 y²+4 x+5 y+1=0 and 3 x²+3 y²+6 x-7 y+3 k=0 are orthogonal, then value of k is

Options

  1. A17 12
  2. B12 17
  3. C- 12 17
  4. D- 17 12

Correct answer

D. - 17 12

Step-by-step solution

Given equation of circles aligned 2 x²+2 y²+4 x+5 y+1 &=0 x²+y²+2 x+5 / 2 y+1 / 2 &=0 (i) 3 x²+3 y²+6 x-7 y+3 k &=0 x²+y²+2 x+7 / 3+k &=0 (ii) aligned Centre and radius of first circle and second circle gathered C₁ (-1,-5 / 4), R₁ 1+ 25 16 -1 / 2 = 16+25-8 16 = 33 16 C₂ (-1,7 / 6), R₂ 1+ 49 36 -k = 85-36 k 36 gathered Now, condition for orthogonality of two circles aligned (C₁ C₂ )² &=R₁ ²+R₂ ² (-1+1)²+(7 / 6+5 / 4)² &= 33 16 + 85-36 k 36 0+ ( 29 12 )² &= 33 16 + 85-36 k 36 aligned aligned 841 144 &= 33 16 + 85-36

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