Home
Class 11
MATHS
Statement 1 : The equation x^2+y^2-2x-2a...

Statement 1 : The equation `x^2+y^2-2x-2a y-8=0` represents, for different values of `a ,` a system of circles passing through two fixed points lying on the x-axis. Statement 2 : `S=0` is a circle and `L=0` is a straight line. Then `S+lambdaL=0` represents the family of circles passing through the points of intersection of the circle and the straight line (where `lambda` is an arbitrary parameter).

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

Prove that the equation x^(2)+y^(2)-2x-2ay-8=0, a in R represents the family of circles passing through two fixed points on x-axis.

The straight line passing through the point of intersection of the straight line x+2y-10=0 and 2x+y+5=0 is

Show that equation x^2+y^2-2ay-8=0 represents, for different values of 'a, asystem of circles"passing through two fixed points A, B on the X-axis, and find the equation ofthat circle of the system the tangents to which at AB meet on the line x+ 2y + 5 = 0 .

Find the equation of the smallest circle passing through the intersection of the line x+y=1 and the circle x^2+y^2=9

The centre of the circle passing through the points (0,0), (1,0) and touching the circle x^2+y^2=9 is

The radius of the circle passing through the points of intersection of ellipse x^2/a^2+y^2/b^2=1 and x^2-y^2 = 0 is

Find the equation of the circle passing through the point ( 2, 3) and touching the line 2x+3y=4 at the point ( 2, 0)

Find the equations of the circles passing through the point (-4,3) and touching the lines x+y=2 and x-y=2

Find the equations of the circles passing through the point (-4,3) and touching the lines x+y=2 and x-y=2

Find the equation of the circle which passes through the points (2,3)(4,2) and the centre lies on the straight line y-4x+3=0.

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Statement 1 : Points A(1,0),B(2,3),C(5,3),a n dD(6,0) are concyclic. S...

    Text Solution

    |

  2. Statement I The chord of contact of tangent from three points A, B and...

    Text Solution

    |

  3. Statement 1 : The equation x^2+y^2-2x-2a y-8=0 represents, for differe...

    Text Solution

    |

  4. The circles having radii r1 and r2 intersect orthogonally. Find the le...

    Text Solution

    |

  5. Tangents P A and P B are drawn to x^2+y^2=9 from any arbitrary poin...

    Text Solution

    |

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

    Text Solution

    |

  7. If the pair of straight lines x ysqrt(3)-x^2=0 is tangent to the circl...

    Text Solution

    |

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

    Text Solution

    |

  9. The condition that the chord xcosalpha+ysinalpha-p=0 of x^2+y^2-a^2=0 ...

    Text Solution

    |

  10. Let the base A B of a triangle A B C be fixed and the vertex C lies...

    Text Solution

    |

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

    Text Solution

    |

  12. Statement : Points (1, 1), (2, 3), and (3, 5) are collinear.

    Text Solution

    |

  13. Statement 1 : The number of circles touching lines x+y=1,2x-y=5, and 3...

    Text Solution

    |

  14. The line 2x-y+1=0 is tangent to the circle at the point (2, 5) and the...

    Text Solution

    |

  15. The equation of the chord of the circle x^2+y^2-3x-4y-4=0 , which pas...

    Text Solution

    |

  16. A rhombus is inscribed in the region common to the two circles x^2+y^2...

    Text Solution

    |

  17. In a triangle A B C , right angled at A , on the leg A C as diameter, ...

    Text Solution

    |

  18. Two congruent circles with centered at (2, 3) and (5, 6) which inter...

    Text Solution

    |

  19. The locus of the center of the circle such that the point (2,3) is t...

    Text Solution

    |

  20. The value of 'c' for which the set {(x,y)|x^2+y^2+2x le 1}nn{(x,y)|x-y...

    Text Solution

    |