Home
Class 11
MATHS
If p and q are the lengths of perpendicu...

If p and q are the lengths of perpendiculars from the origin to the lines `x cos theta - y sin theta = k cos 2 theta " and " x sec theta + y cosec theta = k `, respectively, prove that `p^(2) + 4q^(2) = k^(2)`.

Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    NCERT TAMIL|Exercise Miscellaneous Exercise on Chapter 10|24 Videos

  • STRAIGHT LINES

    NCERT TAMIL|Exercise EXERCISE 10.2|20 Videos

  • STATISTICS

    NCERT TAMIL|Exercise Miscellaneous Exercise On Chapter 15|7 Videos

  • TRIGONOMETRIC FUNCTIONS

    NCERT TAMIL|Exercise MISCELLANEOUS EXAMPLES|10 Videos

Similar Questions

Explore conceptually related problems

If sec theta + tan theta = k, cos theta =

If x sin ^3 theta +y cos^3 theta = sin theta cos theta and x sin theta =y cos theta then x^2 +y^2 is

If xsin^(3) theta +y cos^(3) theta=sin theta cos theta and x sin theta =y cos theta , then prove that x^(2)+y^(2)=1 .

Prove the following: cot^2 theta - tan^2 theta = cosec^2 theta - sec^2 theta

Prove the following: (sin theta - cos theta + 1 )/(sin theta + cos theta - 1) = 1/(sec theta - tan theta)

If "cosec" theta - sin theta = a^(3) and sec theta - cos theta = b^(3) , then prove that a^(2)b^(2)(a^(2) + b^(2))= 1.

Solve : 3-2 cos theta -4 sin theta - cos 2theta+sin 2theta=0 .

Prove that sin^(4) theta + cos^(4) theta = 1 - 2 sin^2 theta cos^(2) theta

NCERT TAMIL-STRAIGHT LINES-EXERCISE 10.3
  1. Reduce the following equations into slope - intercept form and find th...

    Text Solution

    |

  2. Reduce the following equations into intercept form and find their inte...

    Text Solution

    |

  3. Reduce the following equations into normal form. Find their perpendicu...

    Text Solution

    |

  4. Find the distance of the point (-1, 1) from the line 12 (x + 6) = 5 (...

    Text Solution

    |

  5. What are the points on the y-axis whose distance from the linex/3 + y/...

    Text Solution

    |

  6. Find the distance between parallel lines i. 15x+8y-34= 0 and 15x+8y...

    Text Solution

    |

  7. Find equation of the line parallel to the line 3x - 4y + 2 = 0 and pa...

    Text Solution

    |

  8. Find equation of the line perpendicular to the line x - 7y + 5 = 0 an...

    Text Solution

    |

  9. Find angles between the lines sqrt3x + y = 1 " and " x + sqrt3y = 1.

    Text Solution

    |

  10. The line through the points (h, 3) and (4,1) intersects the line 7x -...

    Text Solution

    |

  11. Prove that the line through the point (x(1) , y(1)) and parallel to th...

    Text Solution

    |

  12. Two lines passing through the point (2, 3) intersects each other at an...

    Text Solution

    |

  13. Find the equation of the right bisector of the line segment joining th...

    Text Solution

    |

  14. Find the coordinates of the foot of perpendicular from the point (-1, ...

    Text Solution

    |

  15. The perpendicular from the origin to the line y = mx + c meets it at t...

    Text Solution

    |

  16. If p and q are the lengths of perpendiculars from the origin to the li...

    Text Solution

    |

  17. In the triangle ABC with vertices A (2, 3) , B (4, -1) " and " C (1, ...

    Text Solution

    |

  18. If p is length of perpendicular from the origin to the line whose inte...

    Text Solution

    |