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AP EAMCET202422 May 2024Morning ShiftMathematicsCircleActual

C₁ is the circle with centre at O(0,0) and radius 4, C₂ is a variable circle with centre at ( , ) and radius 5 . If the common chord of C ₁ and C ₂ has slope 3 4 and of maximum length, then one of the possible values of + is

Options

  1. A21 5
  2. B3 5
  3. C1 5
  4. D19 5

Correct answer

B. 3 5

Step-by-step solution

Equation of circle C₁ be x^2+y^2=16 Equation of circle C₂ be (x- )^2+(y- )^2=25 x^2-2 x+ ^2+y^2-2 y+ ^2=25 Equation of common chord is C₂-C₁=0 -2 x-2 y+ ^2+ ^2=9 Slope of common chord = - = 3 4 Let =-3 and =4 Maximum length of common chord is diameter of smaller circle C₁ . So, chord passes through centre of C₂(0,0) . aligned & ^2+ ^2=9 9 ^2+16 ^2=9 = 3 5 & + = -9 5 + 12 5 = 3 5 aligned

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