Home
Class 12
MATHS
Show that, x = (1)/(2)(3+5 cos theta), y...

Show that, `x = (1)/(2)(3+5 cos theta), y = (1)/(2)(-4 + 5 sin theta)` represent a circle passing through the origin. Find the coordinates of centre and length of radius of the circle.

Text Solution

Verified by Experts

The correct Answer is:
`((3)/(2), -1)` and `(5)/(2)` unit
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

Find the coordinates of the centre and the length of radius of the circle 5x^(2)+5y^(2)-8x+6y - 15 = 0

If theta is a variable parameter , show that the equations x=(1)/(4)(3-cosec^(2)theta),y = 2 + cot theta represent the equation of a parabola. Find the coordinates of vertex , focus and the length of latus rectum of the parabola.

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

Find the centre and radius of the circle: (x+5)^2+(y-3)^2=20

Find the equation of the circle through the points (1, -6), (2, 1) and (5, 2), find the coordinates of its centre and the length of the radius.

A circle passes through the points (-6, 5), (-3, -4) and its radius is 5 unit, find the equation of the circle.

The parametric equations of a circle are, x = (1)/(2)(-3+4 cos theta), y = (1)/(2)(1+4 sin theta) . Find the equation of the circle.

3x + y = 5 and x+y+1 = 0 are two diameters to the circle which passes through the point (-2, 2). Find its equation. Also find the radius of the circle.

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

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

    |