Home
Class 11
MATHS
For a gt b gt c gt 0, the distance betwe...

For `a gt b gt c gt 0`, the distance between (1, 1) and the point of intersection of the lines ax+by+c =0 and bx+ay+c=0 is les than `2sqrt(2)`. Then

Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    CENGAGE ENGLISH|Exercise All Questions|508 Videos
  • TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise All Questions|983 Videos

Similar Questions

Explore conceptually related problems

For a gt b gt c gt 0 , if the distance between (1,1) and the point of intersection of the line ax+by-c=0 and bx+ay+c=0 is less than 2sqrt2 then, (A) a+b-cgt0 (B) a-b+clt0 (C) a-b+cgt0 (D) a+b-clt0

A, B C and D are the points of intersection with the coordinate axes of the lines ax+by=ab and bx+ay=ab, then

Let a,b, c and d be non-zero numbers. If the point of intersection of the lines 4ax + 2ay+c=0 and 5bx+2by +d=0 lies in the fourth quadrant and is equidistant from the two axes, then

Prove that distance between two parallel lines ax+by+c_1=0 and ax+by+c_2=0 is given by |c_1-c_2|/(sqrt(a^2+b^2))

Let a gt 0, b gt 0 and c lt0. Then, both the roots of the equation ax^(2) +bx+c=0

The shortest distance between the point (0, 1/2) and the curve x = sqrt(y) , (y gt 0 ) , is:

If a gt 0,bgt 0,cgt0 and 2a +b+3c=1 , then

Show that the distance between the parallel lines ax+by+c=0 and k(ax+by)+d=0 is |(c-(d)/(k))/(sqrt(a^(2)+b^(2)))|

If the direction ratios of two lines are lt a, b, c gt and lt b-c, c-a, a-b gt , find the angle between them.

The shortest distance between the point ((3)/(2),0) and the curve y=sqrt(x),(x gt 0) , is

CENGAGE ENGLISH-STRAIGHT LINES-All Questions
  1. Lines L1-=a x+b y+c=0 and L2-=l x+m y+n=0 intersect at the point P and...

    Text Solution

    |

  2. Let A B C be a triangle with A B=A Cdot If D is the midpoint of B C ,E...

    Text Solution

    |

  3. For a gt b gt c gt 0, the distance between (1, 1) and the point of int...

    Text Solution

    |

  4. A straight line L through the point (3,-2) is inclined at an angle 60^...

    Text Solution

    |

  5. The locus of the orthocentre of the triangle formed by the lines (1+p)...

    Text Solution

    |

  6. The vertices of a triangle are (A(-1,-7),B(5,1), and C(1,4)dot The equ...

    Text Solution

    |

  7. Let the algebraic sum of the perpendicular distance from the points (2...

    Text Solution

    |

  8. A straight line through the origin 'O' meets the parallel lines 4x +2y...

    Text Solution

    |

  9. A straight line l with negative slope passes through (8,2) and cuts th...

    Text Solution

    |

  10. A straight line L through the origin meets the lines x + y = 1 and x +...

    Text Solution

    |

  11. A rectangle PQRS has its side PQ parallel to the line y= mx and verti...

    Text Solution

    |

  12. The area of the triangle formed by the intersection of a line parallel...

    Text Solution

    |

  13. The lines ax + by + c = 0, where 3a + 2b + 4c= 0, are concurrent at th...

    Text Solution

    |

  14. The area enclosed within the curve |x|+|y|=1 is

    Text Solution

    |

  15. Find the orthocentre of the triangle the equations of whose sides are ...

    Text Solution

    |

  16. If a , b and c are in A P , then the straight line a x+b y+c=0 will al...

    Text Solution

    |

  17. Statement-l: If the diagonals of the quadrilateral formed by the lines...

    Text Solution

    |

  18. Statement :Two different lines can be drawn passing through two given ...

    Text Solution

    |

  19. Statement 1: The internal angle bisector of angle C of a triangle A B ...

    Text Solution

    |

  20. The joint equation of lines y=xa n dy=-x is y^2=-x^2, i.e., x^2+y^2=0 ...

    Text Solution

    |