Home
Class 12
MATHS
Prove that the line lx+my+n=0 and the pa...

Prove that the line `lx+my+n=0` and the pair of lines `(lx+my)^2-3(mx-ly)^2=0` form an equilateral triangle and its area is `(n^2)/(sqrt(3)(l^2+m^2))`

Promotional Banner

Topper's Solved these Questions

  • IPE:MARCH-2015 (AP)

    SRISIRI PUBLICATION|Exercise IPE:MARCH-2015(AP) MATHS-1B|22 Videos

  • IPE:MARCH-2015[AP]

    SRISIRI PUBLICATION|Exercise SECTION-C (SAQ)|7 Videos

Similar Questions

Explore conceptually related problems

Show that the lines (x+2a)^2-3y^2=0,x=a form an equilateral triangle.

Show that the lines form an equilateral triangle and find its area (x+2a)^(2)-3y^(2)=0,x-a=0

Show that the lines form an equilateral triangle and find its area x^(2)-4xy+y^(2)=0, x+y-3=0

The area of the equilaterial triangle formed by the pair of lines (ax+by)^(2)-3(bx-ay)^(2)=0 and the line ax+by+c=0 is (c^(2))/(sqrt(3)(a^(2)+b^(2))) sq. units.

Show that the straight lines represented by 3x^2+48xy+23y^2=0,3x-2y+13=0 form an equilateral triangle of area (13)/(sqrt(3)) sq. units

If the pair of lines ax^(2)+2hxy+by^(2)=0 (h^(2) gt ab) orms an equilateral triangle with the line lr + my + n = 0 then (a+3b)(3a+b)=

The area of the triangle formed by pair of line (ax+by)^2-3(bx-ay)^2=0 " and the line " ax+by+c=0 is

Show that following lines forms an equilateral triangle and find its area x^(2)-4xy^(2)=0, x+y-3=0

SRISIRI PUBLICATION-IPE:MARCH-2015(TS)-IPE:MARCH-2015(TS) MATHS-1B
  1. Compute lim(x to a ) (tan(x-a))/(x^2-a^2)(a ne 0).

    Text Solution

    |

  2. Compute lim(x to 0 ) ((e^x-1)/(sqrt(1+x)-1))

    Text Solution

    |

  3. Find the derivative of y=sqrt(2x-3)+sqrt(7-3x).

    Text Solution

    |

  4. Find the derivative of y=Sin^-1((2x)/(1+x^2))

    Text Solution

    |

  5. If y=x^2+3x+6 then find triangley and dy when x=10, trianglex=0.01.

    Text Solution

    |

  6. Verify Rolle's theorem for the function y=f(x)=x^2+4on [-3,3]

    Text Solution

    |

  7. A(5,3) and B(3,-2) are 2 fixed points. Find the equation of locus of P...

    Text Solution

    |

  8. When the axes are rotated through an angle 45^@, the transformed equat...

    Text Solution

    |

  9. A straight line with slope 1 passes through Q(-3,5) and meets the stra...

    Text Solution

    |

  10. If f is given by f(x)={{:(k^(2)x-k,"if "xge1),(2,"if "xlt1):} is a co...

    Text Solution

    |

  11. Find the derivative of x^3 from the first principle.

    Text Solution

    |

  12. A particle is moving along a line according s=f(t)=4t^3-3t^2+5t-1 wher...

    Text Solution

    |

  13. Determine the intervals in which f(x)=2/((x-1))+18x,AAx in R-{0} is st...

    Text Solution

    |

  14. Find the orthocentre of the triangle whose sides are 7x+y-10=0, x-2y+5...

    Text Solution

    |

  15. Prove that the line lx+my+n=0 and the pair of lines (lx+my)^2-3(mx-ly)...

    Text Solution

    |

  16. Find the value if k , if the lines joining the origin with the points ...

    Text Solution

    |

  17. Find the angle between the lines, whose direction cosines are given by...

    Text Solution

    |

  18. Find the derivative of (sinx)^(log x)+x^(sinx).

    Text Solution

    |

  19. IF the tangent at a point on the curve x^(2//3)+y^(2//3)=a^(2//3) inte...

    Text Solution

    |

  20. A window is in the shape of a rectangle surmounted by a semi-circle. I...

    Text Solution

    |