Home
Class 12
MATHS
The equation of a circle which touches ...

The equation of a circle which touches the line y = x at (1 , 1) and having y = x -3 as a normal, is

A

`4x^(2)+4y^(2)-20x+4y+8=0`

B

`x^(2)+y^(2)-2x+4y+8=0`

C

`x^(2)+y^(2)-10x-4y+8=0`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
The equation of the family of circles is
`(x-1)^(2)+(y-1)^(2)+lambda(x-y)=0` ...(i)
Its centre lies on y=x-3.
`:. 1+(lambda)/(2)=1-(lambda)/(2)-3 rArr lambda = - 3`
Putting `lambda = -3` in (i), we obtain
`x^(2)+y^(2)-5x+y+2=0`
Promotional Banner

Topper's Solved these Questions

  • CIRCLES

    OBJECTIVE RD SHARMA|Exercise Section-I (Solved MCQs)|1 Videos

  • CIRCLES

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|12 Videos

  • CIRCLES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|55 Videos

  • CARTESIAN PRODUCT OF SETS AND RELATIONS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|31 Videos

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|59 Videos

Similar Questions

Explore conceptually related problems

Find the equation of the circle which touch the line 2x-y=1 at (1,1) and line 2x+y=4

What is the equation of circle which touches the lines x = 0 , y = 0 and x = 2 ?

Find the equation of the circle which touches the lines x=0 ,y=0 and x=c

The equation of the circle touching the lines |y| = x and having radius sqrt(2) is :

The equation (s) of circle (s) touching 12x - 5y = 7 at (1, 1) and having radius 13 is/are

Find the equations of circles which touch 2x-3y+1=0 at (1,1) and having radius sqrt(13)

Find the equations of the circles touching the lines y=0 and y=sqrt(3) (x+1) and having the centres at a distance 1 from the origin.

Radius of smaller circle that touches the line y=x at (1,1) and also touches the x -axis is:

Find the equation of the circle which touches the axis of: (1)x pass through the point (1,1) and have line x+y=3 as diameter

The equation of circle which touches the line x+3y-2=0 and 3x+9y-2=0, also the point of contact an first line is (-1,1), is

OBJECTIVE RD SHARMA-CIRCLES-Section I - Solved Mcqs
  1. If circles x^(2)+y^(2)+2x+2y+c=0 and x^(2)+y^(2)+2ax+2ay+c=0 where c i...

    Text Solution

    |

  2. A circle is passing through the points A (1, 1) and B (1, 3) and the b...

    Text Solution

    |

  3. The equation of a circle which touches the line y = x at (1 , 1) and ...

    Text Solution

    |

  4. The centres of a set of circles, each of radius 3, lie on the circle x...

    Text Solution

    |

  5. If the lines a1x+b1y+c1=0 and a2x+b2y+c2=0 cut the coordinae axes at c...

    Text Solution

    |

  6. Tangents drawn from the point P(1,8) to the circle x^2 +y^2 -6x -4y-11...

    Text Solution

    |

  7. A variable circle passes through the fixed A (p, q) and touches the x-...

    Text Solution

    |

  8. The centres of two circles C(1) and C(2) each of unit radius are at a...

    Text Solution

    |

  9. Three distinct points A, B and C are given in the 2–dimensional coor...

    Text Solution

    |

  10. In DeltaABC, equation of side BC is x+y-6=0, also the circumcentre and...

    Text Solution

    |

  11. The locus of the middle point of the chord of contact of tangents draw...

    Text Solution

    |

  12. A tangent PT is drawn to the circle x^2 + y^2= 4 at the point P(sqrt3,...

    Text Solution

    |

  13. A common tangent to the circles x^(2)+y^(2)=4 and (x-3)^(2)+y^(2)=1, i...

    Text Solution

    |

  14. If the line y=mx +1 meets the circle x^(2)+y^(2)+3x=0 in two points eq...

    Text Solution

    |

  15. If three distinct point A, B, C are given in the 2-dimensional coordi...

    Text Solution

    |

  16. The common tangents to the circle x^2 + y^2 =2 and the parabola y^2 = ...

    Text Solution

    |

  17. Tangents PA and PB are drawn to the circle x^2 +y^2=8 from any arbitra...

    Text Solution

    |

  18. Given two circles x^2 +y^2+3sqrt(2)(x+y)=0 and x^2 +y^2 +5sqrt(2)(x+y)...

    Text Solution

    |

  19. Let RS be the diameter of the circle x^2+y^2=1, where S is the point (...

    Text Solution

    |

  20. The circle C(1) : x^(2)+y^(2)=3, with cenre at O, intersects the parab...

    Text Solution

    |