Home
Class 11
MATHS
Prove that the pair of straight lines jo...

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`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

The equation of the line joining the origin to the point of intersection of the lines 2x^2+xy-y^2+5x-y+2=0 is

Find the equations of the straight lines joining the origin to the points of intersection of x^2+y^2-4x-2y=4 and x^2+y^2-2x-4y=4 .

Find the equation of the straight line joining the origin to the point of intersection of y-x+7=0 and y+2x-2=0 .

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

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 equation of pair of lines joining origin to the points of intersection of x^2 + y^2 =9 and x + y = 3

The lines joining the origin to the point of intersection of x^2+y^2+2gx+c=0 and x^2+y^2+2fy-c=0 are at right angles if

Find the angle between the straight lines joining the origin to the point of intersection of x^2+2x y+3y^2+4x+8y-11=0 and 3x-y=-2

Find the equation of line joining origin to the point of intersection of the pair of lines 3x+y=10 and x-y=2 .

The lines joining the origin to the points of intersection of the line 3x-2y -1 and the curve 3x^2 + 5xy -3y^2+2x +3y= 0 , are

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Find the length of the common chord of the circles x^2+y^2+2x+6y=0 and...

    Text Solution

    |

  2. If the circle x^(2)+y^(2)=1 is completely contained in the circle x^(2...

    Text Solution

    |

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

    Text Solution

    |

  4. The circles x^2+y^2-12 x-12 y=0 and x^2+y^2+6x+6y=0. a.touch each oth...

    Text Solution

    |

  5. If theta is the angle between the two radii (one to each circle) drawn...

    Text Solution

    |

  6. If the lines a1x+b1y+c1=0 and a2x+b2y+c2=0 cut the coordinae axes at c...

    Text Solution

    |

  7. A line is drawn through a fix point P(alpha, beta) to cut the circle x...

    Text Solution

    |

  8. Circles are drawn through the point (2, 0) to cut intercept of length ...

    Text Solution

    |

  9. Find the equation of the circle passing through the origin and cutting...

    Text Solution

    |

  10. Find the point of intersection of the circle x^2+y^2-3x-4y+2=0 with th...

    Text Solution

    |

  11. Find the values of k for which the points (2k ,3k),(1,0),(0,1),a n d(0...

    Text Solution

    |

  12. If one end of the diameter is (1, 1) and the other end lies on the lin...

    Text Solution

    |

  13. Tangent drawn from the point P(4,0) to the circle x^2+y^2=8 touches it...

    Text Solution

    |

  14. If the join of (x1,y1) and (x2,y2) makes on obtuse angle at (x3,y3), t...

    Text Solution

    |

  15. Find the range of values of m for which the line y=m x+2 cuts the circ...

    Text Solution

    |

  16. Centre of the circle whose radius is 3 and which touches internally th...

    Text Solution

    |

  17. Find the number of common tangents that can be drawn to the circles...

    Text Solution

    |

  18. Find the radical center of the circles x^2+y^2+4x+6y=19 ,x^2+y^2=9,x^2...

    Text Solution

    |

  19. Two circles C1 and C2 intersect in such a way that their common chord ...

    Text Solution

    |

  20. The equation of a circle is x^2+y^2=4. Find the center of the smallest...

    Text Solution

    |