Home
Class 12
MATHS
Show that the locus of the point of inte...

Show that the locus of the point of intersection of the lines `x cos alpha + y sin alpha = a` and `x sin alpha - y cos alpha = a`, when `alpha` varies, is a circle.

Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    CHHAYA PUBLICATION|Exercise Exercise 3 (Long Answer Type Questions)|25 Videos

  • CIRCLE

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (MCQs)|5 Videos

  • CIRCLE

    CHHAYA PUBLICATION|Exercise Exercise 3 (Very Short Answer Type Questions)|18 Videos

  • CALCULUS

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive (2014)|2 Videos

  • COMPLEX NUMBER

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTION FOR COMPETITIVE EXAMS(Multiple Corrrect Answer type)|11 Videos

Similar Questions

Explore conceptually related problems

Locus of mid-point of the portionof the line x cos alpha + y sin alpha =p between the coordinate axes is-

Show that the image of the point (h,k) with respect to the striaight line x cos alpha+ y sin alpha=p is the point (2 p cos alpha- h cos2 alpha- k sin 2 alpha, 2p sin alpha- h sin 2 alpha- k cos 2 alpha) .

The lines x cos alpha + y sin alpha = p_1 and x cos beta + y sin beta = p_2 will be perpendicular, if :

Find the locus of the mid - point of the portion of the line x cos alpha + y sin alpha = 4 intercepted between the axes of coordinates .

sin alpha + sin beta = a "and" cos alpha + cos beta = b sin (alpha + beta) =

If sin alpha = sin beta and cos alpha = cos beta then-

Prove that, 1/3 ( cos^(3) alpha sin 3 alpha + sin^(3) alpha cos 3 alpha) = 1/4 sin 4 alpha

sin alpha + sin beta = a "and" cos alpha + cos beta = b cos (alpha + beta) =

If A=[(cos alpha, -sin alpha),(sin alpha, cos alpha)], and A+A'=I , then the value of alpha is

CHHAYA PUBLICATION-CIRCLE-Exercise 3 (Short Answer Type Questions)
  1. A circle touches y-axis at (0, 5) and whose centre lies on the line 2x...

    Text Solution

    |

  2. Find the equation of a circle which passes through the point (4, 2) an...

    Text Solution

    |

  3. Two cirles of radii 2 and 10 units respectively pass through (2, 4) an...

    Text Solution

    |

  4. Prove that the point (-1, -2) lies on the circle x^(2) + y^(2) - x y -...

    Text Solution

    |

  5. Show that for all values of p, the circle x^(2) + y^(2) - x(3p+4) - y(...

    Text Solution

    |

  6. Find the coordinates of points equidistant from the axes and lying on ...

    Text Solution

    |

  7. Find the equation to the common chord of the two circles x^(2) + y^(2)...

    Text Solution

    |

  8. Find the equation of the common chord of the two circles x^(2)+y^(2)-4...

    Text Solution

    |

  9. Find the equation of the circles which passes through the origin and t...

    Text Solution

    |

  10. A point moves in such a manner that the sum of the squares of its dist...

    Text Solution

    |

  11. A(3, 0) and B(-3, 0) are two given points and P is a moving point : if...

    Text Solution

    |

  12. Show that the locus of the point of intersection of the lines x cos al...

    Text Solution

    |

  13. Whatever be the values of theta, prove that the locus of the point of ...

    Text Solution

    |

  14. Show that, x = (1)/(2)(3+5 cos theta), y = (1)/(2)(-4 + 5 sin theta) r...

    Text Solution

    |

  15. Prove that the square of the distance between the two points (x(1), y(...

    Text Solution

    |

  16. The equations of two diameters of a circle are x-2y+1 = 0 and x+y -2 =...

    Text Solution

    |

  17. Find the equation of the circle circumscribing the rectangle whose sid...

    Text Solution

    |

  18. A and B are two fixed points on a plane and P moves on the plane in su...

    Text Solution

    |

  19. Show that the equation of the circle described on the chord x cos alph...

    Text Solution

    |

  20. Find the circumcentre and circumradius of the triangle formed by the l...

    Text Solution

    |