Home
Class 11
MATHS
If p(1) and p(2) are the lengths of the ...

If `p_(1) and p_(2)` are the lengths of the perpendicular form the orgin to the line `x sec theta+y cosec theta=a and xcostheta-y sin theta=a cos 2 theta` respectively then prove that `4p_(1)^(2)+p_(2)^(2)=a^(2)`

A

`sqrt(m)`

B

m

C

`m^(2)`

D

`m^(4)`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINE

    MARVEL PUBLICATION|Exercise MISCELLANEOUS MCQS|160 Videos

  • STRAIGHT LINE

    MARVEL PUBLICATION|Exercise MISCELLANEOUS MCQS|160 Videos

  • SETS, RELATIONS AND FUNCTIONS

    MARVEL PUBLICATION|Exercise MCQs|139 Videos

  • TRIGONOMETRIC FUNCTIONS

    MARVEL PUBLICATION|Exercise MCQs|175 Videos

Similar Questions

Explore conceptually related problems

If p and q are the lengths of perpendicular from the origin to the line x cos(theta)-y sin(theta)=k cos(2 theta) and x sec(theta)+y cos ec(theta)=k respectively,then prove that p^(2)+4q^(2)=k^(2)

If p and q are the lengths of perpendiculars from the origin to the lines x cos theta-y sin theta=k cos2 theta and x sec theta+y csc theta=k respectively,prove that quad p^(2)+4q^(2)=k^(2)

If p and p_1 be the lengths of the perpendiculars drawn from the origin upon the straight lines x sin theta + y cos theta = 1/2 a sin 2 theta and x cos theta - y sin theta = a cos 2 theta , prove that 4p^2 + p^2_1 = a^2 .

If p and q are respectively the perpendiculars from the origin upon the straight lines, whose equations are x sec theta + y cosec theta =a and x cos theta -y sin theta = acos 2 theta , then 4p^(2) + q^(2) is equal to

If x=p sec theta+q tan theta&y=p tan theta+q sec theta then prove that x^(2)-y^(2)=p^(2)-q^(2)

If x=cosec theta-sin theta and y=sec theta-cos theta then prove that x^(2/3)+y^(2/3)=(xy)^(-2/3)

MARVEL PUBLICATION-STRAIGHT LINE-MUTIPLE CHOICE QUESTIONS
  1. A point of the X-axis which is at a unit distance from the line 5x+12y...

    Text Solution

    |

  2. If the perpendicular distance of the line (x/a)+(y/b)=1 from the origi...

    Text Solution

    |

  3. If p(1) and p(2) are the lengths of the perpendicular form the orgin t...

    Text Solution

    |

  4. In relation to the line : (x)/(3)-(y)/(4)=1, the point (-2,-4) lies on

    Text Solution

    |

  5. In relation to the line : 7(x-2) =5(y+3), the point (3,-2) lies on

    Text Solution

    |

  6. If the line passing through (2,3) and (5,k) has slope (5/3), then : k=

    Text Solution

    |

  7. If the points (-3,4), (-14,12) and (8,k) are collinear then :k

    Text Solution

    |

  8. If the point (3,k) lies on the line passing through the points (-1,3) ...

    Text Solution

    |

  9. If the triangle whose vertices are A(4,3), B(6,-2) and C(k,-3) is righ...

    Text Solution

    |

  10. If A is (5,-3) and B is a point on the X-axis such that the slope of l...

    Text Solution

    |

  11. If A is (-4,9) and B is a point on the Y-axis such that the slope of t...

    Text Solution

    |

  12. If A is (1,-2), B (3,k), C(-3,1) and D (k,4) where lines AB and CD are...

    Text Solution

    |

  13. If A is (1,-2), B (3,k), C(-3,1) and D(k,4) where lines ABbot CD then ...

    Text Solution

    |

  14. If the point (1,1) lies on the line passing through the points (a,0)...

    Text Solution

    |

  15. The slope of the line which bisects the angles in the first and third ...

    Text Solution

    |

  16. The slope of the line which bisects the angles in the second and fourt...

    Text Solution

    |

  17. If A (1,-2), B (-2,3) and C(2,-5) are the vertices of Delta ABC, then ...

    Text Solution

    |

  18. The equation of the line which passes through (4,7) and divides the jo...

    Text Solution

    |

  19. The equation of the line having inclination 120^(@) and dividing the j...

    Text Solution

    |

  20. The area of the quadrilateral whose sides are along the lines x=0, x=4...

    Text Solution

    |