Home
Class 11
MATHS
A variable circle passes through the poi...

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`

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

A variable circle passes through the fixed point A(p,q) and touches the x-axis. The locus of the other end of the diameter through A is-

A variable plane passes through a fixed point (a,b,c) and meets the axes at A ,B ,a n dCdot The locus of the point commom to the planes through A ,Ba n dC parallel to the coordinate planes 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 point (-2, 1) and touches the straight line 3x - 2y = 6 at the point (4, 3) . Find its equation.

The circle passing through (1, - 2) and touching the axis of x at (3, 0) also passes through the point

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

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

The circle passing through (1 , -2) and touching the axis of x at (3 , 0) also passes through the point _

A variable line passes through the fixed point (alpha,beta) . The locus of the foot of the perpendicular from the origin on the line is,

A variable plane passes through a fixed point (a ,b ,c) and cuts the coordinate axes at points A ,B ,a n dCdot Show that locus of the centre of the sphere O A B Ci s a/x+b/y+c/z=2.

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Find the locus of the midpoint of the chords of the circle x^2+y^2-ax-...

    Text Solution

    |

  2. Let the lines (y-2)=m1(x-5) and (y+4)=m2(x-3) intersect at right angle...

    Text Solution

    |

  3. A variable circle passes through the point A(a, b) and touches the x-a...

    Text Solution

    |

  4. Find the equation of the circle if the chord of the circle joining (1,...

    Text Solution

    |

  5. Find the equation of the circle which passes through (1, 0) and (0, 1)...

    Text Solution

    |

  6. Tangents are drawn from the origin to the circle x^2+y^2-2h x-2h y+h^2...

    Text Solution

    |

  7. Let A (-2,2)and B (2,-2) be two points AB subtends an angle of 45^@ at...

    Text Solution

    |

  8. Consider the family of circles x^2+y^2-2x-2lambday-8=0 passing throug...

    Text Solution

    |

  9. If a circle passes through the point (0,0),(a ,0)a n d(0, b) , then fi...

    Text Solution

    |

  10. The line 3x+6y=k intersects the curve 2x^2+3y^2=1 at points A and B . ...

    Text Solution

    |

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

    Text Solution

    |

  12. If x , y in R satisfies (x+5)^2+(y-12)^2=(14)^2, then the minimum val...

    Text Solution

    |

  13. Show that a cyclic quadrilateral is formed by the lines 5x+3y=9,x=3y ,...

    Text Solution

    |

  14. A circle x^2+y^2+4x-2sqrt(2)y+c=0 is the director circle of the circle...

    Text Solution

    |

  15. A point P moves in such a way that the ratio of its distance from two ...

    Text Solution

    |

  16. The sum of the slopes of the lines tangent to both the circles x^2+y^2...

    Text Solution

    |

  17. Prove that the maximum number of points with rational coordinates on a...

    Text Solution

    |

  18. Let C1 and C2 are circles defined by x^2+y^2 -20x+64=0 and x^2+y^2+...

    Text Solution

    |

  19. Prove that for all values of theta , the locus of the point of interse...

    Text Solution

    |

  20. The chord of contact of tangents from a point P to a circle passes thr...

    Text Solution

    |