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=K^2` orthogonally then the equation of the locus of its centre is

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

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 circle passes through the points (-3, 4), (1, 0) and its centre lies on the x-axis. Find the equation of the circle.

A circle passes through the origin and has its center on y=x If it cuts x^2+y^2-4x-6y+10=0 orthogonally, then find the equation of the circle.

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

A circle passes through the points (3, 4), (-1, 2) and its radius is 5 unit, find the equation of the circle.

A variable circle passes through the point A(a, b) and touches the x-axis. Show that the locus of the other end of the diameter through A is (x-a)^2 = 4by

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

The equations of a diameter of a circle is 2x - y + 4 = 0 and it passes through the points (4, 6) and (1, 9). Find the equation of the circle, the coordinates of its centre and length of its radius.

A circle passes through(1,-2) and (4,-3) and its.centre lies on the straight line 3x + 4y= 7. Find the equation of the circle.-

From the origin, chords are drawn to the circle (x-1)^2 + y^2 = 1 . The equation of the locus of the mid-points of these chords

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Two circles C1a n dC2 both pass through the points A(1,2)a n dE(2,1) a...

    Text Solution

    |

  2. A circle C1 of radius b touches the circle x^2 + y^2 =a^2 externally a...

    Text Solution

    |

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

    Text Solution

    |

  4. Difference in the values of the radius of a circle whose center is at ...

    Text Solution

    |

  5. A triangle is inscribed in a circle of radius 1. The distance between ...

    Text Solution

    |

  6. Find the equation of the circle whose radius is 5 and which touches th...

    Text Solution

    |

  7. Let 2 x^2 + y^2 - 3xy = 0 be the equation of pair of tangents drawn fr...

    Text Solution

    |

  8. Find the equation of a circle which passes through the point (2,0) a...

    Text Solution

    |

  9. Let C1 be the circle with center O1(0,0) and radius 1 and C2 be the ci...

    Text Solution

    |

  10. C1 is a circle of radius 1 touching the x- and the y-axis. C2 is anoth...

    Text Solution

    |

  11. There are two circles whose equation are x^2+y^2=9 and x^2+y^2-8x-6y+n...

    Text Solution

    |

  12. State whether the statement is True or False: The line x+3y=0 is a dia...

    Text Solution

    |

  13. Prove That : No tangent can be drawn from the point (5/2,1) to the cir...

    Text Solution

    |

  14. A circle passes through the points A(1,0) and B(5,0), and touches the ...

    Text Solution

    |

  15. Prove that the locus of the point that moves such that the sum of the ...

    Text Solution

    |

  16. The equation of four circles are (x+-a)^2+(y+-a)^2=a^2 . The radius of...

    Text Solution

    |

  17. An isosceles triangle ABC inscribed in a circle x^2+y^2=a^2 with the v...

    Text Solution

    |

  18. A region in the x-y plane is bounded by the curve y=sqrt(25-x^2) and t...

    Text Solution

    |

  19. If (alpha,beta) is a point on the circle whose center is on the x-axi...

    Text Solution

    |

  20. The area of the triangle formed by joining the origin to the points of...

    Text Solution

    |