AP EAMCET202418 May 2024Morning ShiftMathematicsCircleActual
If is the angle between the tangents drawn from the point (2,3) to the circle x^2+y^2-6 x+4 y+12=0 , then =
Options
- A⁻¹ ( 5 13 )
- B⁻¹ ( 4 5 )
- C2 ⁻¹ ( 5 12 )
- D⁻¹ ( 5 12 )
Correct answer
D. ⁻¹ ( 5 12 )
Step-by-step solution
Given the equation of circle aligned & x^2+y^2-6 x+4 y+12=0 & (x-3)^2+(y+2)^2=1 aligned Since, A O= (3-2)^2+(-2-3)^2 = 1+25 = 26 and, A P= 26-1 =5 Now, in AOP , = 1 5 = ⁻¹ ( 1 5 ) Required angle =2 =2 ⁻¹ ( 1 5 )= ⁻¹ ( 2 5 1- ( 1 5 )^2 )= ⁻¹ ( 10 24 )= ⁻¹ ( 5 12 )