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AP EAMCET202124 Aug 2021Morning ShiftMathematicsCircleActual

If the length of the tangent drawn from the point from (-2,3) to the circle x^2+y^2+8 x-6 y+k=0 is 4 units, then k is equal to

Options

  1. A34
  2. B36
  3. C38
  4. D37

Correct answer

D. 37

Step-by-step solution

Circle C: x^2+y^2+8 x-6 y+k=0 Length of tangents drawn by an external points to the circle is S₁ . Now, the length of tangent drawn by (-2,3) to the circle is L , aligned & & L & = S₁ & & L & = (-2)^2+(3)^2+8(-2)-6(3)+ k & & 4 & = 4+9-16-18+k where L=4 & & 4 & = k-21 16=k-21 & & k & =16+21 k=37 aligned

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