Home
Class 11
MATHS
If the equation of a circle is lambdax^2...

If the equation of a circle is `lambdax^2+(2lambda-3)y^2-4x+6y-1=0,` then the coordinates of centre are

Text Solution

AI Generated Solution

To find the coordinates of the center of the circle given by the equation \[ \lambda x^2 + (2\lambda - 3)y^2 - 4x + 6y - 1 = 0, \] we will follow these steps: ...
Promotional Banner

Topper's Solved these Questions

  • STATISTICS

    RD SHARMA|Exercise Solved Examples And Exercises|175 Videos

  • THE STRAIGHT LINES

    RD SHARMA|Exercise Solved Examples And Exercises|488 Videos

Similar Questions

Explore conceptually related problems

If equation of a circle is (4a - 3) x^(2) +ay^(2) + 6x - 2y + 2 = 0 , then its centre is

Find the parametric equation of the circles : 3x^2 + 3y^2 + 4x-6y - 4 = 0

The equation of the normal at (1,2) to the circle x^(2)-y^(2)-4x-6y-12=0 is

If (-(1)/(3),-1) is a centre of similitude for the circles x^(2)+y^(2)=1 and x^(2)+y^(2)-2x-6y-6=0, then the length of common tangent of the circles is

Find the equation of the circle which is concentric with the circle x^2 +y^2 - 4x+6y-3=0 and the double of its area.

Find the equation of the tangent to the circle x^(2)+y^(2)-30x+6y+109=0 at (4,-1)

Find the equation of the circle concentric with the circle x^(2)+y^(2)-4x-6y-3=0 and which touches the y axis

Find the centre and the radius of the circles 2x^(2) + lambda xy + 2y^(2) + (lambda - 4) x+6y - 5 = 0 , for some lambda

(i) Find the equation of a circle , which is concentric with the circle x^(2) + y^(2) - 6x + 12y + 15 = 0 and of double its radius. (ii) Find the equation of a circle , which is concentric with the circle x^(2) + y^(2) - 2x - 4y + 1 = 0 and whose radius is 5. (iii) Find the equation of the cricle concentric with x^(2) + y^(2) - 4x - 6y - 3 = 0 and which touches the y-axis. (iv) find the equation of a circle passing through the centre of the circle x^(2) + y^(2) + 8x + 10y - 7 = 0 and concentric with the circle 2x^(2) + 2y^(2) - 8x - 12y - 9 = 0 . (v) Find the equation of the circle concentric with the circle x^(2) + y^(2) + 4x - 8y - 6 = 0 and having radius double of its radius.

RD SHARMA-THE CIRCLE-Solved Examples And Exercises
  1. Find the equation of the circle which passes through the points (2,"""...

    Text Solution

    |

  2. If 2x^2+lambdax y^+2y^2+(lambda-4)x+6y-5=0, is the equation of a circ...

    Text Solution

    |

  3. If the equation of a circle is lambdax^2+(2lambda-3)y^2-4x+6y-1=0, th...

    Text Solution

    |

  4. If the line l x+m y+n=0 touches the circle x^2+y^2=a^2 , then prove th...

    Text Solution

    |

  5. Find the equation of the circle which passes through the origin and...

    Text Solution

    |

  6. Prove that the locus of a point which moves such that the sum of th...

    Text Solution

    |

  7. Find the equation of the circle on the straight line joining the poi...

    Text Solution

    |

  8. If a circle of constant radius 3c passes through the origin and meets ...

    Text Solution

    |

  9. Find the equation to the circle which passes through the points (1,...

    Text Solution

    |

  10. Find the equation of the circle, the coordinates of the end points ...

    Text Solution

    |

  11. If the circles x^2+y^2+2a x+c=0a n dx^2+y^2+2b y+c=0 touch each other,...

    Text Solution

    |

  12. Find the equation of the circle which passes through the points (1,-2)...

    Text Solution

    |

  13. The equation of the circle which touches the axes of coordinates an...

    Text Solution

    |

  14. Find the equation of the circle which passes through the points (2,...

    Text Solution

    |

  15. The number of integral values of lambda for which the equation x^2+y^2...

    Text Solution

    |

  16. Find the equation of the circle which touches the lines 4x-3y+10=0a...

    Text Solution

    |

  17. If the line y=sqrt(3)x+k touches the circle x^2+y^2=16 , then find t...

    Text Solution

    |

  18. Find the equation of the circle having (1,-2) as its centre and passi...

    Text Solution

    |

  19. Find the locus of the centre of the circle touching the line x+2y=0 ...

    Text Solution

    |

  20. Let C be any circle with centre (0,sqrt(2))dot Prove that at most two ...

    Text Solution

    |