Home
Class 12
MATHS
A triangle has two of its sides along th...

A triangle has two of its sides along the lines `y=m_1x&y=m_2x` where `m_1, m_2` are the roots of the equation `3x^2+10 x+1=0` and `H(6,2)` be the orthocentre of the triangle. If the equation of the third side of the triangle is `a x+b y+1=0` , then `a=3` (b) `b=1` (c) `a=4` (d) `b=-2`

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

A triangle has two sides y=m_(1)x and y=m_(2)x where m_(1) and m_(2) are the roots of the equation b alpha^(2)+2h alpha+a=0. If (a,b) be the orthocenter of the triangle,then find the equation of the third side in terms of a,b and h.

A triangle has the lines y=m_(1)x and y=m_(2)x for two of its sides,where m_(1),m_(2) are the roots of the equation quad x2+ax-1=0, then find the orthocentre of triangle.

Find the orthocentre of the triangle the equations or whose sides are x+y=1,2x+3y=6 and 4x-y+4=0

nd (, The eqn of two sides of a triangle are 3x-2y + 6-0 and 4x + 5y = 20 and the orthocentre is (1,1). Find the equation of the thired side.

If two sides of a triangle lie along 3x^(2)-5xy+2y^(2)=0 and its orthocenter is (2,1) then the equation to the third side is

The equations of two sides of a triangle are 3x-2y+6=0 and 4x+5y-20 and the orthocentre is (1,1). Find the equation of the third side.

If m_(1) and m_(2) are the roots of the equation x^(2)-ax-a-1=0 then the area of the triangle formed by the three straight lines y=m_(1)xy=m_(2)x and y=a is

If m_(1),m_(2) be the roots of the equation x^(2)+(sqrt(3)+2)x+sqrt(3)-1 =0 , then the area of the triangle formed by the lines y = m_(1)x,y = m_(2)x and y = 2 is

Two sides of a triangle are y=m_(1)x and y=m_(2)x and m_(1),m_(2), are the roots of the equation x^(2)+ax-1=0. For all values of a, the orthocentre of the triangle lies at (A)(1,1) (B) (2,2) (C) ((3)/(2),(3)/(2)) (D) (0,0)

RESONANCE DPP-JEE MAINS-All Questions
  1. Suppose a1,a2, real numbers, with a1!=0, If a1,a2,a3 are in AdotPdo...

    Text Solution

    |

  2. Consider the function f(x)={(1-a^x+x a^x ln a)/(a^xx^2); x<0(2^xa^x-x ...

    Text Solution

    |

  3. A triangle has two of its sides along the lines y=m1x&y=m2x where m1, ...

    Text Solution

    |

  4. The three vectors hat i+ hat j , hat j+ hat k , hat k+ hat i taken tw...

    Text Solution

    |

  5. The number of integer values of m , for which the x-coordinate of the ...

    Text Solution

    |

  6. If A^2+A+I=0 , then A is non-singular A!=0 (b) A is singular A^(-...

    Text Solution

    |

  7. Tangent and normal to the curve y=2s in x+s in2x are drawn at p(x=pi/3...

    Text Solution

    |

  8. If D=|[1/z,1/z,-(x+y)/(z^2)],[-(y+z)/(x^2),1/x,1/x],[-(y(y+z)/(x^2z))...

    Text Solution

    |

  9. The curve y=x^3+x^2-x has two horizontal tangents. The distance betwee...

    Text Solution

    |

  10. The exhaustive domain of f(x)=sqrt(x^(12)-x^9+x^4-x+1) is

    Text Solution

    |

  11. The point of intersection of tangent to the curve y=x^4 at (1,1) with ...

    Text Solution

    |

  12. Equation of straight line a x+b y+c=0 , where 3a+4b+c=0 , which is at ...

    Text Solution

    |

  13. Tangents are drawn from the point P(1,-1) to the circle x^2+y^2-4x-6y-...

    Text Solution

    |

  14. If A=[(1,2,2),(2,1,2),(2,2,10] then (A) A^-1= 1/5(A-4I3) (B) A^2-4A-5I...

    Text Solution

    |

  15. The derivative of (log)(10)x w.r.t. x^2 is equal to 1/(2x^2)loge 10 (...

    Text Solution

    |

  16. If A=[1 2 0-1 1 2 2-1 1],t h e ndet(A d j(A d jA))= 13 (b) 13^2 (c) ...

    Text Solution

    |

  17. Which of the following limits tends to unity? (a) ("lim")(xvec0)sin(ta...

    Text Solution

    |

  18. The algebraic sum of the perpendicular distances from A(x1, y1), B(x2,...

    Text Solution

    |

  19. If sum(k=1)^(k=n)tan^(- 1)(2k)/(2+k^2+k^4)=tan^(- 1)(6/7), then the va...

    Text Solution

    |

  20. The solution set of the inequation 3^(72)(1/3)^x(1/3)^(sqrt(x))&gt;1 ...

    Text Solution

    |