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AP EAMCET2016MathematicsCircle

The angle between the tangents drawn from the origin to the circle x^2+y^2+4 x-6 y+4=0 is

Options

  1. A⁻¹ ( 5 13 )
  2. B⁻¹ ( 5 12 )
  3. C⁻¹ ( -12 2 )
  4. D⁻¹ ( 13 2 )

Correct answer

C. ⁻¹ ( -12 2 )

Step-by-step solution

We have, x^2+y^2+4 x-6 y+4=0 Centre (-g,-f) (-2,3) Radius of circle, OA = g^2+f^2-c aligned & = (2)^2+(-3)^2-4 & = 4+9-4 =3 aligned Length of tangent aligned & PA = PB & = (0)^2+(0)^2+4(0)-6(0)+4 & = 4 =2 aligned In OAP , = O A P A = 3 2 Now, the angle between the tangent drawn from origin aligned & 2 = ⁻¹ ( 2 1- ^2 ) & 2 = ⁻¹ ( 2 3 2 1- 9 4 ) & 2 = ⁻¹ ( -12 5 ) aligned

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