Home
Class 12
MATHS
If the line xcostheta+ysintheta=2 is the...

If the line `xcostheta+ysintheta=2` is the equation of a transverse common tangent to the circles `x^2+y^2=4` and `x^2+y^2-6sqrt(3)x-6y+20=0` , then the value of `theta` is (a)`(5pi)/6` (b) `(2pi)/3` (c) `pi/3` (d) `pi/6`

A

`5pi //6`

B

`2pi //3`

C

`pi //3`

D

`pi//6`

Text Solution

Verified by Experts

The correct Answer is:
3
`C_(1)-=(0,0),C_(2)-=(3sqrt(3),3)`
and `r_(1)=2,r_(2)=4`
`:. C_(1)C_(2)=r_(1)+r_(2)`
Thus, circle touch each other externally .
The equation of common tangent at P is
`sqrt(3) x +y-4=0` (1)
Comparing it with ` r cos theta +y sin theta = 2` , we get `theta = pi //6`
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

Find the equations to the common tangents of the circles x^2+y^2-2x-6y+9=0 and x^2+y^2+6x-2y+1=0

Find the length of the common chord of the circles x^2+y^2+2x+6y=0 and x^2+y^2-4x-2y-6=0

Equation of a common tangent to the circle x^(2) + y^(2) - 6x = 0 and the parabola, y^(2) = 4x , is

The line tangent to the curves y^3-x^2y+5y-2x=0 and x^2-x^3y^2+5x+2y=0 at the origin intersect at an angle theta equal to pi/6 (b) pi/4 (c) pi/3 (d) pi/2

Find the number of common tangents that can be drawn to the circles x^2+y^2-4x-6y-3=0 and x^2+y^2+2x+2y+1=0

If the tangent at the point P(theta) to the ellipse 16 x^2+11 y^2=256 is also a tangent to the circle x^2+y^2-2x=15 , then theta= (a) (2pi)/3 (b) (4pi)/3 (c) (5pi)/3 (d) pi/3

If y=(x^4-x^2+1)/(x^2+sqrt(3)x+1)a n d(dy)/(dx)=a x+b , then the value of a+b is (a) cot(pi/8) (b) cot(pi/12) (c) tan((5pi)/12) (d) tan((5pi)/8)

IF the lengths of the side of triangle are 3,5A N D7, then the largest angle of the triangle is pi/2 (b) (5pi)/6 (c) (2pi)/3 (d) (3pi)/4

The angle subtended by common tangents of two ellipses 4(x-4)^2+25 y^2=100a n d4(x+1)^2+y^2=4 at the origin is (a) pi/3 (b) pi/4 (c) pi/6 (d) pi/2

CENGAGE-CIRCLE -Exercise (Single)
  1. Find the locus of the centres of the circle which cut the circles x^2+...

    Text Solution

    |

  2. Tangent are drawn to the circle x^2+y^2=1 at the points where it is me...

    Text Solution

    |

  3. If the line xcostheta+ysintheta=2 is the equation of a transverse comm...

    Text Solution

    |

  4. about to only mathematics

    Text Solution

    |

  5. The circles having radii r1a n dr2 intersect orthogonally. The length ...

    Text Solution

    |

  6. The two circles which pass through (0,a)a n d(0,-a) and touch the line...

    Text Solution

    |

  7. Locus of thews of the centre of the circle which touches x^2+y^2 - 6x-...

    Text Solution

    |

  8. If the chord of contact of tangents from a point P to a given circle p...

    Text Solution

    |

  9. If the angle of intersection of the circle x^2+y^2+x+y=0 and x^2+y^2+x...

    Text Solution

    |

  10. The coordinates of two points Pa n dQ are (x1,y1)a n d(x2,y2)a n dO is...

    Text Solution

    |

  11. If the circumference of the circle x^2 + y^2 + 8x + 8y - b = 0 is bise...

    Text Solution

    |

  12. Equation of the circle which cuts the circle x^2+y^2+2x+ 4y -4=0 and ...

    Text Solution

    |

  13. The minimum radius of the circle which contains the three circles, x^...

    Text Solution

    |

  14. A circle C1 of radius b touches the circle x^2 + y^2 =a^2 externally a...

    Text Solution

    |

  15. Find the locus of centre of variable circle C, that rouches the circle...

    Text Solution

    |

  16. The centre of the smallest circle touching the circles x^2+ y^2-2y -3=...

    Text Solution

    |

  17. Two circle with radii r(1) and r(2) respectively touch each other exte...

    Text Solution

    |

  18. Consider points A(sqrt13,0) and B(2sqrt13,0) lying on x-axis. These po...

    Text Solution

    |

  19. The common chord of the circle x^2+y^2+6x+8y-7=0 and a circle passing ...

    Text Solution

    |

  20. If the circumference of the circle x^2+y^2+8x+8y-b=0 is bisected by th...

    Text Solution

    |