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MHT CET2010MathematicsCircle

The equations of the tangents to the circle x²+y²-6 x+4 y=12 , which are parallel to the straight line 4 x+3 y+5=0 , are

Options

  1. A3 x-4 y-19=0,3 x-4 y+31=0
  2. B4 x+3 y-19=0,4 x+3 y+31=0
  3. C4 x+3 y+19=0,4 x+3 y-31=0
  4. D3 x-4 y+19=0,3 x-4 y+31=0

Correct answer

C. 4 x+3 y+19=0,4 x+3 y-31=0

Step-by-step solution

Let equation of tangent be 4 x+3 y+k=0 centre of the circle is (3,-2) . Then, 9+4+12 = | 4(3)+3(-2)+k 16+9 | 6+k= 25 k=19 and -31 Hence, the tangent are 4 x+3 y+19=0 and 4 x+3 y-31=0

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