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)`.

Text Solution

Verified by Experts

The correct Answer is:
`=k^2`
which is required result.
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    KUMAR PRAKASHAN|Exercise Exercise : 10.4|4 Videos

  • STRAIGHT LINES

    KUMAR PRAKASHAN|Exercise Exercise : 10.5|8 Videos

  • STRAIGHT LINES

    KUMAR PRAKASHAN|Exercise Exercise : 10.2|20 Videos

  • STATISTICS

    KUMAR PRAKASHAN|Exercise QUESTION OF MODULE (KNOWLEDGE TEST)|9 Videos

  • TRIGONOMETRIC FUNCTIONS

    KUMAR PRAKASHAN|Exercise QUESTION OF MODULE (KNOWLEDGE TEST)|15 Videos

Similar Questions

Explore conceptually related problems

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

P_1 and P_2 are the length of perpendicular from origin to the line x sec theta + y cosec theta =a and x cos theta - y sin theta = a cos 2 theta then ….... of the following is valid.

If cos theta + sin theta = p and sec theta + cosec theta = q , prove that q (p^(2) - 1) = 2p .

Find length of perpendicular from origin to the lines passes from points ( cos theta , sin theta ) and ( cos phi , sin phi) .

Find perpendicular distance from the origin to the line joining the points ( cos theta , sin theta ) and ( cos phi, sin phi) .

If cosec theta + cot theta =k , then prove that cos theta =(k^(2)-1)/( k^(2)+1)

If costheta + sin theta = sqrt2 cos theta , prove that cos theta - sin theta = sqrt2 sin theta .

If x +y= 3-cos4theta and x-y=4sin2theta then

Evaluate the following (sin theta +cos theta )^(2) +(sin theta -cos theta )^(2)

Minimum value of the expression cos^2theta-(6 sintheta cos theta) + 3 sin^2theta + 2 , is

KUMAR PRAKASHAN-STRAIGHT LINES-Exercise : 10.3
  1. Reduce the following equations in intercept form and find their interc...

    Text Solution

    |

  2. Reduce the following equation in normal form. Find their perpendicular...

    Text Solution

    |

  3. Reduce the following equation in normal form. Find their perpendicular...

    Text Solution

    |

  4. Reduce the following equation in normal form. Find their perpendicular...

    Text Solution

    |

  5. Find the distance of the point (-1, 1) from the line 12(x+6) = 5(y-2).

    Text Solution

    |

  6. Find the points on the X-axis, whose distances from the line (x)/(3) +...

    Text Solution

    |

  7. Find the distance between following pair of parallel lines : (i) 15x...

    Text Solution

    |

  8. Find the distance between following pair of parallel lines : (ii) l(...

    Text Solution

    |

  9. Find equation of the line parallel to the line 3x-4y+2=0 and passing t...

    Text Solution

    |

  10. Find equation of the line perpendicular to the line x-7y+5=0 and havin...

    Text Solution

    |

  11. Find angles between the lines sqrt(3) x +y=1 and x+ sqrt(3) y=1.

    Text Solution

    |

  12. The line through the points (h,3) and (4,1) intersects the line 7x-9y-...

    Text Solution

    |

  13. Prove that the line through the point (x1, y1) and parallel to the lin...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. Find the coordinates of the foot of perpendicular from the point (-1,3...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. In the triangle ABC with vertices A(2,3), B(4,1) and C(1,2), find the ...

    Text Solution

    |

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

    Text Solution

    |