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

If `P_(1) and p_(2)` are the lenghts of the perpendiculars drawn from the origin to the two lines
x sec `alpha` +y . Cosec `alpha` =2a
and x. cos `alpha` +y. sin `alpha`=a. cos 2 `alpha`,
show that `P_(1)^(2)+P_(2)^(2)` is constant for all values of `alpha` .

Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINE

    MARVEL PUBLICATION|Exercise MUTIPLE CHOICE QUESTIONS|78 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 p' are the distances of the origin from the lines x "sec" alpha + y " cosec" alpha = k " and " x "cos" alpha-y " sin" alpha = k "cos" 2alpha, " then prove that 4p^(2) + p'^(2) = k^(2).

If p&q are lengths of perpendicular from the origin x sin alpha+y cos alpha=a sin alpha cos alpha and x cos alpha-y sin alpha=a cos2 alpha, then 4p^(2)+q^(2)

If p_(1) and p_(2) ,be the lengths of the perpendiculars from theorigin upon the lines 4x+3y=5cos alpha and 6x8y=5sin alpha respectively,show that,p_(1)^(2)+4p_(2)^(2)=1

Find the length of perpendicular from the point (a cos alpha, a sin alpha) to the line x cos alpha+y sin alpha=p .

The foot of the perpendicular from (0,0) to the line x cos alpha+y sin alpha=p is

If x sin ^ (3) alpha + y cos ^ (3) alpha = sin alpha cos alpha and x sin alpha-y cos alpha = 0 then x ^ (2) + y ^ (2) =

If cos alpha + cos 2alpha = p , sin alpha + sin 2alpha = q then eliminate alpha .

If the line y cos alpha = x sin alpha +a cos alpha be a tangent to the circle x^(2)+y^(2)=a^(2) , then

MARVEL PUBLICATION-STRAIGHT LINE-MISCELLANEOUS MCQS
  1. If P(1) and p(2) are the lenghts of the perpendiculars drawn from the ...

    Text Solution

    |

  2. If the point P(p,q) is equidistant from the points A(a+b,b-a)and B(a-b...

    Text Solution

    |

  3. Prove that the points (a+b+c),(b,c+a) and (c,a+b) are collinear.

    Text Solution

    |

  4. Points A (a,3) and C (5,b) are opposite vertices of a rectangle ABCD. ...

    Text Solution

    |

  5. If a,b,c are non-zero real numbers in H.P then the line (x)/(a)+(y)/(...

    Text Solution

    |

  6. Let A (2,-3) and B(-2,1) be vertices of a triangle ABC. If the centroi...

    Text Solution

    |

  7. For any real values of a,b,c such that 3a, +2b+4c=0, line ax+by+c=0 pa...

    Text Solution

    |

  8. The equations of sides of a triangle are x+3y=0 , 4x-3y=5 and 3x-y=0....

    Text Solution

    |

  9. Ifa,b,c are in A.P., a,x,b,are in G.P and b,y,c are also in G.P then t...

    Text Solution

    |

  10. If we reduce 3x+3y+7=0 to the form xcosalpha+ysinalpha=p , then find t...

    Text Solution

    |

  11. The length of perpendicular from the point ( a cos prop, a sin prop) ...

    Text Solution

    |

  12. the line x/a-y/b=1 cuts the x-axes at P.the equation of the line passe...

    Text Solution

    |

  13. If (-4,5) is a vertex of a square and one of its diagonal is 7x-y+8-0....

    Text Solution

    |

  14. If a,b,c gt 0, then area of the triangle formed by the line ax+by+c=0 ...

    Text Solution

    |

  15. If the line ax+by+c=0 always passes through the fixed point (1,-2) th...

    Text Solution

    |

  16. A square of area 25 sq.units is formed by taking two sides as 3x + 4y ...

    Text Solution

    |

  17. Segment joining (1,2) and (-2,1) is divided by the line 3x+4y=7 in the...

    Text Solution

    |

  18. The medians AD and BE of the triangle with vertices A(0, b), B(0, 0) a...

    Text Solution

    |

  19. A triangle are (6,0).(0, 6) and (6,6). If distance between circumcentr...

    Text Solution

    |

  20. If a vertex of a triangle is (1,1) , and the middle points of two side...

    Text Solution

    |

  21. Find the points on the line x+y=4 that lies at a unit distance from th...

    Text Solution

    |