Home
Class 12
MATHS
find the area of the quadrilateral forme...

find the area of the quadrilateral formed by a pair of tangents from the point (4,5) to the circle `x^2 + y^2 -4x -2y-11 = 0` and pair of its radii.

A

`4 sq. units`

B

`8 sq. units`

C

`6 sq. units`

D

`16 sq. units`

Text Solution

Verified by Experts

The correct Answer is:
B
The area of the ………….

Area of quadilateral `OAPB`
`= 2xxDelta OAP`
`= 2xx (1)/(2)xxAPxxOA`
`= APxxOA` ……….(1)
`AP = sqrt(16+25-16-10-11) = sqrt(41-37) = 2`
`OA = r = sqrt(4+1+11) = 4`
Area of quadrilateral `= 2xx4=8`
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    RESONANCE|Exercise PART : 1MATHEMATICS SEC - 1|1 Videos

  • TEST PAPERS

    RESONANCE|Exercise PART : 1MATHEMATICS|9 Videos

  • TEST PAPER

    RESONANCE|Exercise CHEMISTRY|37 Videos

  • TEST SERIES

    RESONANCE|Exercise MATHEMATICS|131 Videos

Similar Questions

Explore conceptually related problems

The pair of tangents from (2,1) to the circle x^(2)+y^(2)=4 is

If the area of the quadrilateral formed by the tangent from the origin to the circle x^(2)+y^(2)+6x10y+c=0 and the pair of radii at the points of contact of these tangents to the circle is 8 sq.units,then c is a root of the equation

Find the equation of the tangent at the point (0,2) to the circle x^2+y^2-4x+2y-8=0

The angle between the pair of tangents from the point (1,(1)/(2)) to the circle x^(2)+y^(2)+4x+2y-4=0 is

The pair of tangents from origin to the circle x^(2)+y^(2)+4x+2y+3=0 is

The equation of pair of tangents drawn from the point (0,1) to the circle x^(2) + y^(2) – 2x + 4y = 0 is–

The angle between the pair of tangents drawn from the point (2,4) to the circle x^(2)+y^(2)=4 is

Find the area of the triangle formed by the tangents from the point (4,3) to the circle x^(2)+y^(2)=9 and the line joining their points of contact.

RESONANCE-TEST PAPERS-MATHEMATICS
  1. find the area of the quadrilateral formed by a pair of tangents from t...

    Text Solution

    |

  2. The least positive integral value of 'k' for which there exists at lea...

    Text Solution

    |

  3. The locus of the midpoint of a chord of the circle x^2+y^2=4 which sub...

    Text Solution

    |

  4. If f(x)=x+tanx and g(x) is inverse of f(x) then g^(')(x) is equal to

    Text Solution

    |

  5. Tangents PA and PB are drawn to parabola y^(2)=4x from any arbitrary p...

    Text Solution

    |

  6. If lim(nrarroo) (n.2^(n))/(n(3x-4)^(n)+n.2^(n+1)+2^(n))=1/2 where "n" ...

    Text Solution

    |

  7. Eccentricity of ellipse 2(x-y+1)^(2)+3(x+y+2)^(2)=5 is

    Text Solution

    |

  8. If (tan^(-1)x)^(3)+(tan^(-1)y)^(3)=1-3tan^(-1)x.tan^(-1)y. Then which ...

    Text Solution

    |

  9. If f:RrarrR is a continuous function satisfying f(0)=1 and f(2x)-f(x)=...

    Text Solution

    |

  10. tan^(-1)(sinx)=sin^(-1)(tanx) holds true for

    Text Solution

    |

  11. is The function f(x)=(x^2-1)|x^2-3x+2|+cos(|x|) is differentiable not ...

    Text Solution

    |

  12. Consider parabola P(1)-=y=x^(2) and P(2)-=y^(2)=-8x and the line L-=lx...

    Text Solution

    |

  13. If the normals at (x(i),y(i)) i=1,2,3,4 to the rectangular hyperbola x...

    Text Solution

    |

  14. Let f(x)=x^(3)-x^(2)+x+1 and g(x)={("max "f(t) 0letlex 0lexle1),(3-x 1...

    Text Solution

    |

  15. The value(s) of x satisfying tan^(-1)(x+3)-tan^(-1)(x-3)=sin^(-1)(3/5)...

    Text Solution

    |

  16. For an ellipse having major and minor axis along x and y axes respecti...

    Text Solution

    |

  17. If f:[0,1]rarrR is defined as f(x)={(x^(3)(1-x)"sin"1/(x^(2)) 0ltxle1)...

    Text Solution

    |

  18. If f(x)=root (3)(8x^(3)+mx^(2))-nx such that lim(xrarroo)f(x)=1 then

    Text Solution

    |

  19. For the curve y=4x^3-2x^5,find all the points at which the tangent pa...

    Text Solution

    |

  20. Minimum value of (sin^(-1)x)^(2)+(cos^(-1)x)^(2) is greater than

    Text Solution

    |

  21. If y+a=m(1)(x+3a),y+a=m(2)(x+3a) are two tangents to the parabola y^(2...

    Text Solution

    |