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AP EAMCET2008MathematicsCircle

If is the angle between the tangents from (-1,0) to the circle x^2+y^2-5 x+4 y-2=0 , then is equal to

Options

  1. A2 ⁻¹ ( 7 4 )
  2. B⁻¹ ( 7 4 )
  3. C2 ⁻¹ ( 7 4 )
  4. D⁻¹ ( 7 4 )

Correct answer

A. 2 ⁻¹ ( 7 4 )

Step-by-step solution

We know that, the angle between the two tangents from ( , ) to the circle x^2+y^2=r^2 is 2 ⁻¹ r S₁ Given equation of circle is x^2+y^2-5 x+4 y-2=0 . Now, radius, r= (- 5 2 )^2+(2)^2+2 = 49 4 = 7 2 At point (-1,0) aligned S₁ & =(-1)^2+(0)^2-5(-1)+4(0)-2 & =1+5-2=4 aligned Required angle, =2 ⁻¹ 7 2 4 =2 ⁻¹ ( 7 4 )

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