Home
Class 12
MATHS
Line a x+b y+p=0 makes angle pi/4 with c...

Line `a x+b y+p=0` makes angle `pi/4` with `cosalpha+ycosalpha+ysinalpha=p ,p in R^+` . If these lines and the line `xsinalpha-ycosalpha=0` are concurrent, then `a^2+b^2=1` (b) `a^2+b^2=2` `2(a^2+b^2)=1` (d) none of these

A

`a^(2)+b^(2)=1`

B

`a^(2)+b^(2)=2`

C

`2(a^(2)+b^(2))=1`

D

`a^(2)+b^(2)=3`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    AAKASH INSTITUTE|Exercise ASSIGNMENT (SECTION C) (OBJECTIVE TYPE QUESTIONS) (MORE THAN ONE ANSWER)|14 Videos

  • STRAIGHT LINES

    AAKASH INSTITUTE|Exercise ASSIGNMENT (SECTION D) (LINKED COMPREHENSION TYPE QUESTIONS)|12 Videos

  • STRAIGHT LINES

    AAKASH INSTITUTE|Exercise ASSIGNMENT (SECTION A) (OBJECTIVE TYPE QUESTIONS) (ONLY ONE ANSWER)|50 Videos

  • STATISTICS

    AAKASH INSTITUTE|Exercise Section-C Assertion-Reason|15 Videos

  • THREE DIMENSIONAL GEOMETRY

    AAKASH INSTITUTE|Exercise ASSIGNMENT SECTION - J|10 Videos

Similar Questions

Explore conceptually related problems

Line ax+by+p=0 makes angle (pi)/(4) with x cos alpha+y sin alpha=p,p in R^(+). If these lines and the line x sin alpha-y cos alpha=0 are concurrent,then a^(2)+b^(2)=1( b) a^(2)+b^(2)=22(a^(2)+b^(2))=1( d) none of these

If the lines ax+2y+1=0,bx+3y+1=0 and cx+4y+1=0 are concurrent,then a,b,c are in A.P.( b) G.P.( c) H.P.(d) None of these

I the lines a x+12 y+1=0,\ b x+13 y+1=0 and c x+14 y+1=0 are concurrent, then a , b , c are in a. H.P. b. G.P. c. A.P. d. none of these

If p be the length of theperpendicular from the origin on the line x//a+y//b =1, then p^2=a^2+b^2 b. p^2=1/(a^2)+1/(b^2) c. 1/(p^2)=1/(a^2)+1/(b^2) d. none of these

If the lines ax+by+p=0x cos alpha+y sin alpha-p=0(p!=0) and x sin alpha-y sin alpha=0 are concurrent and the first two lines include an angle (pi)/(4), then a^(2)+b^(2) is equal to

If the lines x +3y -9 = 0, 4x + by -2 = 0 and 2x -y -4 = 0 are concurrent , the b is equal to

2a+b+2c=0(a,b,c in R), then the family of lines ax+by+c=0 is concurrent at

Find Angle between two line x sinalpha+ycosalpha=p_(1) and x sin B +ycosB=p_(2)" "(alpha gt beta)

If the lines ax+2y+1=0,bx+3y+1=0 and cx+4y+1=0 are concurrent,then a,b,c are in a.A.P.b.G.P.c.H.P. d.none of these

If the straight line xcosalpha+ysinalpha=p touches the curve (x^2)/(a^2)+(y^2)/(b^2)=1 , then prove that a^2\ cos^2alpha+b^2\ s in^2alpha=p^2 .

AAKASH INSTITUTE-STRAIGHT LINES-ASSIGNMENT (SECTION B) (OBJECTIVE TYPE QUESTIONS) (ONLY ONE ANSWER)
  1. The line 5x + 4y = 0 passes through the point of intersection of strai...

    Text Solution

    |

  2. The equation of the base of an equilateral triangle is x+y=2 and its v...

    Text Solution

    |

  3. A ray of light is sent along the line which passes through the point (...

    Text Solution

    |

  4. Line a x+b y+p=0 makes angle pi/4 with cosalpha+ycosalpha+ysinalpha=p ...

    Text Solution

    |

  5. Find the image of the point (-8,12) with respect to line mirror 4x+7y+...

    Text Solution

    |

  6. in a triangle ABC, if A is (1, 2) and the equations of the medians thr...

    Text Solution

    |

  7. The equation of straight line equally inclined to the axes and equidis...

    Text Solution

    |

  8. A line passing through (0,0) and perpendicular to 2x+y+6=0,4x+2y-9=0 t...

    Text Solution

    |

  9. The centroid of the triangle formed by the pair of straight lines 12x^...

    Text Solution

    |

  10. If x^2-2p x y-y^2=0 and x^2-2q x y-y^2=0 bisect angles between each ot...

    Text Solution

    |

  11. If a , ba n dc are in A P , then the straight line a x+b y+c=0 will al...

    Text Solution

    |

  12. The straight line ax + by = 1 makes with the curve px^2 + 2axy + qy^2 ...

    Text Solution

    |

  13. the lines L1 and L2 denoted by 3x^2 + 10xy +8y^2 +14x +22y + 15 =...

    Text Solution

    |

  14. The equation of the lines through the origin and which are perpendicul...

    Text Solution

    |

  15. A ray of light is sent along the line x-2y-3=0 on reaching the line 3x...

    Text Solution

    |

  16. The mid-point of the line segment joirning (3, -1) and (1, 1) is shift...

    Text Solution

    |

  17. Sum of the possible values of lamda for which the following threes lin...

    Text Solution

    |

  18. The ends A and B of a straight line segment of constant length c slide...

    Text Solution

    |

  19. The value of h for which 3x^2-2hxy + 4y^2 = 0 represents a pair of coi...

    Text Solution

    |

  20. Distance between the pari of straight lines x^(2)+6xy+9y^(2)+4x+12y-5=...

    Text Solution

    |