Home
Class 11
MATHS
If a circle passes through the point (a,...

If a circle passes through the point (a, b) and cuts the circle `x^2+ y^2 = p^2` orthogonally, then the equation of the locus of its centre is :

A

`2ax + 2by -(a^2-b^2+ p^2)= 0`

B

`x^2+ y^2- 3ax-4by + (a^2+b^2- p^2)= 0`

C

`2ax + 2by - (a^2+b^2+ p^2)= 0`

D

`x^2+ y^2-2ax-3by + (a^2-b^2-p^2)= 0`.

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    MODERN PUBLICATION|Exercise EXERCISE|478 Videos
  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise EXERCISE|291 Videos
  • INFINITE SERIES

    MODERN PUBLICATION|Exercise EXAMPLE|10 Videos

Similar Questions

Explore conceptually related problems

If a circle Passes through a point (a,b) and cut the circle x^2+y^2 = 4 orthogonally,Then the locus of its centre is

A circle of constant radius a passes through the origin O and cuts the axes of coordinates at points P and Q . Then the equation of the locus of the foot of perpendicular from O to P Q is

The angle between a pair of tangents from a point P to the circle x^2 + y^2 = 25 is pi/3 . Find the equation of the locus of the point P.

A circle S passes through the point (0, 1) and is orthogonal to the circles (x -1)^2 + y^2 = 16 and x^2 + y^2 = 1 . Then (A) radius of S is 8 (B) radius of S is 7 (C) center of S is (-7,1) (D) center of S is (-8,1)

The normal at the point (3,4) on a circle cuts the circle at the poins (-1,-2) . Then the equation of the circle is

The circle passing through the point ( -1,0) and touching the y-axis at (0,2) also passes through the point.

Find the equation of the circle passing through the point of intersection of the circles x^2 + y^2 - 6x + 2y + 4 = 0, x^2 + y^2 + 2x - 4y -6 = 0 and with its centre on the line y = x.

Two perpendicular tangents to the circle x^2 + y^2= a^2 meet at P. Then the locus of P has the equation

The equation of the circle passing through the point (1, 1) and through the points of intersection of the circles : x^2+ y^2=6 and x^2+ y^2-6y+8=0 is :

A circle passes through point (3, sqrt(7/2)) and touches the line-pair x^2 - y^2 - 2x +1 = 0 . Centre of circle lies inside the circle x^2 + y^2 - 8x + 10y + 15 = 0 . Coordinates of centre of circle are given by

MODERN PUBLICATION-CONIC SECTIONS-EXERCISE
  1. If the circles : x^2+ y^2+2ax + cy +a=0 and x^2+ y^2-3ax+dy -1=0 inter...

    Text Solution

    |

  2. A circle touches the X-axis and also touches the centre at (0,3) and r...

    Text Solution

    |

  3. If a circle passes through the point (a, b) and cuts the circle x^2+ y...

    Text Solution

    |

  4. An ellipse has OB as semi minor axis, F and F' its focii eccentricity ...

    Text Solution

    |

  5. The locus of a point P(alpha, beta) moving under the condition that th...

    Text Solution

    |

  6. A circle is given by x^2 + (y-1)^2 = 1, another circle C touches it ex...

    Text Solution

    |

  7. The minimum area of the triangle formed by the tangent to (x^2)/(a^2)+...

    Text Solution

    |

  8. A straight line through the point A(3,4) is such that its intercept be...

    Text Solution

    |

  9. If (a,a^(2)) falls inside the angle made by the lines y = x/2 , x gt ...

    Text Solution

    |

  10. If the lines 3x - 4y- 7 = 0 and 2x - 3y- 5 = 0 are two diameters of a ...

    Text Solution

    |

  11. Let C be the circle with centre (0, 0) and radius 3 units. The equatio...

    Text Solution

    |

  12. The locus of the vertices of the family of parabolas y=(a^3x^2)/3+(a^2...

    Text Solution

    |

  13. Angle between the tangents to the curve y=x^2-5x+6 at the points (2,0)...

    Text Solution

    |

  14. The axis of a parabola is along the line y=x and the distance of its v...

    Text Solution

    |

  15. The equation of the common tangents to the parabola y = x^2 and y=- (x...

    Text Solution

    |

  16. Let a hyperbola passes through the focus of the ellipse (x^(2))/(25)-(...

    Text Solution

    |

  17. If one of the lines of my^2+(1-m^2) xy-mx^2=0 is a bisector of the ang...

    Text Solution

    |

  18. Let ABCD be a quadrilateral with area 18, with side AB parallel to the...

    Text Solution

    |

  19. Consider a family of circles which are passing through the point (-1,1...

    Text Solution

    |

  20. The equation of a tangent to the parabola y^2=""8x""i s""y""=""x""+"...

    Text Solution

    |