Home
Class 11
MATHS
The tangent at any point P on the circle...

The tangent at any point `P` on the circle `x^2+y^2=4` meets the coordinate axes at `A and B` . Then find the locus of the midpoint of `A Bdot`

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

The tangent at P , any point on the circle x^2 +y^2 =4 , meets the coordinate axes in A and B , then (a) Length of AB is constant (b) PA and PB are always equal (c) The locus of the midpoint of AB is x^2 +y^2=x^2y^2 (d) None of these

The tangent at any point P on the circle x^2 + y^2 = 2 cuts the axes in L and M . Find the locus of the middle point of LM .

Find the eqution of the curve passing through the point (1,1), if the tangent drawn at any point P(x,y) on the curve meets the coordinate axes at A and B such that P is the mid point of AB.

Consider an ellipse (x^2)/4+y^2=alpha(alpha is parameter >0) and a parabola y^2=8x . If a common tangent to the ellipse and the parabola meets the coordinate axes at Aa n dB , respectively, then find the locus of the midpoint of A Bdot

The tangent at any point to the circle x^(2)+y^(2)=r^(2) meets the coordinate axes at A and B. If the lines drawn parallel to axes through A and B meet at P then locus of P is

If a tangent to the circle x^(2)+y^(2)=1 intersects the coordinate axes at distinct points P and Q, then the locus of the mid-point of PQ is :

The tangent at any point on the curve x=acos^3theta,y=asin^3theta meets the axes in Pa n dQ . Prove that the locus of the midpoint of P Q is a circle.

The tangent at any point on the curve x=acos^3theta,y=asin^3theta meets the axes in Pa n dQ . Prove that the locus of the midpoint of P Q is a circle.

A variable straight line is drawn through the point of intersection of the straight lines x/a+y/b=1 and x/b+y/a=1 and meets the coordinate axes at A and Bdot Show that the locus of the midpoint of A B is the curve 2x y(a+b)=a b(x+y)

The tagents at any point P of the circle x^(2)+y^(2)=16 meets the tangents at a fixed point A at T. Point is joined to B, the other end of the diameter, through, A. The sum of focal distance of any point on the curce is

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Find the length of the tangent drawn from any point on the circle x^2+...

    Text Solution

    |

  2. Find the locus of a point which moves so that the ratio of the lengths...

    Text Solution

    |

  3. The tangent at any point P on the circle x^2+y^2=4 meets the coordinat...

    Text Solution

    |

  4. If a line passing through the origin touches the circle (x-4)^2+(y+5)^...

    Text Solution

    |

  5. If the chord of contact of the tangents drawn from the point (h , k) t...

    Text Solution

    |

  6. If the straight line x - 2y + 1 = 0 intersects the circle x^2 + y^2 = ...

    Text Solution

    |

  7. If the chord of contact of the tangents drawn from a point on the ci...

    Text Solution

    |

  8. The lengths of the tangents from any point on the circle 15x^(2)+15y^(...

    Text Solution

    |

  9. Find the equation of the normal to the circle x^2+y^2=9 at the point (...

    Text Solution

    |

  10. Find the equations of tangents to the circle x^2+y^2-22 x-4y+25=0 whic...

    Text Solution

    |

  11. If the length tangent drawn from the point (5, 3) to the circle x^2...

    Text Solution

    |

  12. A pair of tangents are drawn from the origin to the circle x^2+y^2+20(...

    Text Solution

    |

  13. Find the equation of the normal to the circle x^2+y^2-2x=0 parallel to...

    Text Solution

    |

  14. Find the equation of the tangent to the circle x^2+y^2+4x-4y+4=0 which...

    Text Solution

    |

  15. If the distances from the origin of the centers of three circles x^2+y...

    Text Solution

    |

  16. Find the equation of the normals to the circle x^2+y^2-8x-2y+12=0 at t...

    Text Solution

    |

  17. An infinite number of tangents can be drawn from (1,2) to the circle x...

    Text Solution

    |

  18. If the circle x^2+y^2-4x-8y-5=0 intersects the line 3x-4y=m at two dis...

    Text Solution

    |

  19. The line A x+B y+C=0 cuts the circle x^2+y^2+a x+b y+c=0 at Pa n dQ . ...

    Text Solution

    |

  20. Find the equation of the circle which cuts the three circles x^2+y^2-3...

    Text Solution

    |