Home
Class 11
MATHS
A triangle is formed by the lines x+y=0,...

A triangle is formed by the lines `x+y=0,x-y=0,` and `l x+m y=1.` If `l` and `m` vary subject to the condition `l^2+m^2=1,` then the locus of its circumcenter is (a) `(x^2-y^2)^2=x^2+y^2` (b) `(x^2+y^2)^2=(x^2-y^2)` (c) `(x^2+y^2)^2=4x^2y^2` (d) `(x^2-y^2)^2=(x^2+y^2)^2`

Text Solution

AI Generated Solution

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

A triangle is formed by the lines x+y=0,x-y=0, and l x+m y=1. If la n dm vary subject to the condition l^2+m^2=1, then the locus of its circumcenter is (a) (x^2-y^2)^2=x^2+y^2 (b) (x^2+y^2)^2=(x^2-y^2) (c) (x^2+y^2)^2=4x^2y^2 (d) (x^2-y^2)^2=(x^2+y^2)^2

Add : x^(2) y^(2) , 2x^(2)y^(2) , - 4x^(2)y^(2) , 6x^(2)y^(2)

The locus of the foot of perpendicular drawn from the centre of the ellipse x^2+""3y^2=""6 on any tangent to it is (1) (x^2-y^2)^2=""6x^2+""2y^2 (2) (x^2-y^2)^2=""6x^2-2y^2 (3) (x^2+y^2)^2=""6x^2+""2y^2 (4) (x^2+y^2)^2=""6x^2-2y^2

The locus of the foot of the perpendicular from the center of the hyperbola x y=1 on a variable tangent is (a) (x^2+y^2)^2=4x y (b) (x^2-y^2)=1/9 (x^2-y^2)=7/(144) (d) (x^2-y^2)=1/(16)

The factors of x^3-x^2y-x y^2+y^3 are (a (x+y)(x^2-x y+y^2) (b) (x+y)(x^2+x y+y^2) (c) (x+y)^2(x-y) (d) (x-y)^2(x+y)

The locus of the foot of the perpendicular from the center of the hyperbola x y=1 on a variable tangent is (x^2+y^2)^2=4x y (b) (x^2-y^2)=1/9 (x^2-y^2)=7/(144) (d) (x^2-y^2)=1/(16)

(x+y)^3−(x−y)^3 can be factorized as (a) 2y(3x^2+y^2) (b) 2x(3x^2+y^2) (c) 2y(3y^2+x^2) (d) 2x(x^2 +3y^2)

If points A and B are (1, 0) and (0, 1), respectively, and point C is on the circle x^2+y^2=1 , then the locus of the orthocentre of triangle A B C is x^2+y^2=4 x^2+y^2-x-y=0 x^2+y^2-2x-2y+1=0 x^2+y^2+2x-2y+1=0

The factors of x^3-1+y^3+3x y are (a) (x-1+y)(x^2+1+y^2+x+y-x y) (b) (x+y+1)(x^2+y^2+1-x y-x-y) (c) (x-1+y)(x^2-1-y^2+x+y+x y) (d) 3(x+y-1)(x^2+y^2-1)

Find the condition for the line y=m x to cut at right angles the conic a x^2+2h x y+b y^2=1.

CENGAGE ENGLISH-STRAIGHT LINES-All Questions
  1. If the equation of the locus of a point equidistant from the points (a...

    Text Solution

    |

  2. The extremities of the base of an isosceles triangle are (2,0)a n d(0,...

    Text Solution

    |

  3. A triangle is formed by the lines x+y=0,x-y=0, and l x+m y=1. If l a...

    Text Solution

    |

  4. The line x+y=p meets the x- and y-axes at Aa n dB , respectively. A ...

    Text Solution

    |

  5. A is a point on either of two lines y+sqrt(3)|x|=2 at a distance of ...

    Text Solution

    |

  6. A pair of perpendicular straight lines is drawn through the origin f...

    Text Solution

    |

  7. If the vertices Pa n dQ of a triangle P Q R are given by (2, 5) and (4...

    Text Solution

    |

  8. Given A-=(1,1) and A B is any line through it cutting the x-axis at ...

    Text Solution

    |

  9. The straight lines 4a x+3b y+c=0 , where a+b+c are concurrent at the ...

    Text Solution

    |

  10. The line parallel to the x-axis and passing through the intersection o...

    Text Solution

    |

  11. The line L1:""y""-""x""=""0 and L2:""2x""+""y""=""0 intersect the line...

    Text Solution

    |

  12. If the lines a x+y+1=0,x+b y+1=0, and x+y+c=0(a , b , c being distinct...

    Text Solution

    |

  13. Two sides of a rhombus ABCD are parallel to the lines y = x + 2 and y ...

    Text Solution

    |

  14. Equation(s) of the straight line(s), inclined at 30^(@) to the x-axis ...

    Text Solution

    |

  15. If a pair of perpendicular straight lines drawn through the origin ...

    Text Solution

    |

  16. The sides of a rhombus are parallel to the lines x+y-1=0 and 7x-y-5=0....

    Text Solution

    |

  17. The image of P(a ,b) on the line y=-x is Q and the image of Q on t...

    Text Solution

    |

  18. Consider a DeltaABC whose sides AB, BC and CA are represented by the s...

    Text Solution

    |

  19. The equations of two equal sides A Ba n dA C of an isosceles triangle ...

    Text Solution

    |

  20. Find the area of the triangle formed by the line x+y=3 and the angle b...

    Text Solution

    |