Home
Class 11
MATHS
Prove that the straight lines joining th...

Prove that the straight lines joining the origin to the points of intersection of the straight line `hx+ky=2hk` and the curve `(x-k)^(2)+(y-h)^(2)=c^(2)` are at right angle if `h^(2)+k^(2)=c^(2)`.

Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    CENGAGE PUBLICATION|Exercise All Questions|507 Videos

  • TRIGONOMETRIC FUNCTIONS

    CENGAGE PUBLICATION|Exercise All Questions|986 Videos

Similar Questions

Explore conceptually related problems

The angle between the lines joining the origin to the points of intersection of the line sqrt3x+y=2 and the curve y^(2)-x^(2)=4 is

Find the condition for which the lines joining the origin to the points of intersection of the line y= mx+c and the circle x^2+y^2=a^2 will be mutually bot

Prove that the angle between the lines joining the origin to the points of intersection of the straight line y=3x+2 with the curve x^2+2x y+3y^2+4x+8y-11=0 is tan^(-1)((2sqrt(2))/3)

Find the angle between the straight lines joining the origin to the point of intersection of 3x^2+5x y-3y^2+2x+3y=0 and 3x-2y=1

The pair of straight lines joining the origin to the points of intersection of X^2+Y^2=4 and y=3X +c are perpendicular, if frac(c^2)(4) =

Prove that the pair of straight lines joining the origin to the points of intersection of the circles x^2+y^2=a and x^2+y^2+2(gx+fy)=0 is a^(prime)(x^2+y^2)-4(gx+fy)^2=0

The straight line joining the points (-3,-4) and(2,5) is -

Prove that, The line 5x + 4y = 0 passes through the point of intersection of straight lines x+2y-10 = 0, 2x + y =-5

The limiting position of the point of intersection of the straight lines 3x+5y=1 and (2+c)x+5c^2y=1 as c tends to one is:

Find the equation of the bisectors of the angles between the lines joining the origin to the point of intersection of the straight line x-y=2 with the curve 5x^2+11 x y+8y^2+8x-4y+12=0

CENGAGE PUBLICATION-STRAIGHT LINES-All Questions
  1. The pair of lines joining the origin to the points of intersection of ...

    Text Solution

    |

  2. Find the angle between the lines joining the origin to the points of i...

    Text Solution

    |

  3. Prove that the straight lines joining the origin to the points of inte...

    Text Solution

    |

  4. If pairs of straight lines x^2-2pxy-y^2=0and x^2-2qxy-y^2=0 be such th...

    Text Solution

    |

  5. Find the value of a for which the lines represented by ax^(2)+5xy+2y^(...

    Text Solution

    |

  6. Find the acute angle between the pair of lines represented by (xcosalp...

    Text Solution

    |

  7. If the angle between the lines represented by 2x^2+5xy+3y^2+7x+13y-3=0...

    Text Solution

    |

  8. If the pair of straight lines ax^(2)+2hxy+by^(2)=0 is rotated about th...

    Text Solution

    |

  9. The orthocenter of the triangle formed by the lines xy=0 and x+y=1 is

    Text Solution

    |

  10. The lines joining the origin to the point of intersection of 3x^(2)+...

    Text Solution

    |

  11. If the slope of one line is double the slope of another line and the c...

    Text Solution

    |

  12. Find the combined equation of the pair of lines through the point (1,0...

    Text Solution

    |

  13. The value k for which 4x^(2)+8xy+ky^(2)=9 is the equation of a pair of...

    Text Solution

    |

  14. The two lines represented by 3ax^(2)+5xy+(a^(2)-2)y^(2)=0 are perpendi...

    Text Solution

    |

  15. If two lines represented by x^4+x^3y+c x^2y^2-x y^3+y^4=0 bisector of ...

    Text Solution

    |

  16. The straight lines represented by x^2+m x y-2y^2+3y-1=0 meet at (a) (-...

    Text Solution

    |

  17. The straight lines represented by the equation 135 x^2-136 x y+33 y^2=...

    Text Solution

    |

  18. If one of the lines of my^(2)+(1-m^(2))xy-mx^(2)=0 is a bisector of th...

    Text Solution

    |

  19. Statement 1 : If -2h=a+b , then one line of the pair of lines a x^2+...

    Text Solution

    |

  20. Show that all chords of the curve 3x^(2)-y^(2)-2x+4y=0, which subtend...

    Text Solution

    |