Home
Class 11
MATHS
If a ne b ne c, prove that (a, a^2), (b,...

If `a ne b ne c`, prove that `(a, a^2), (b, b^2), (c, c^2)` can never be collinear.

Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    MODERN PUBLICATION|Exercise EXERCISE|478 Videos

  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise EXERCISE|291 Videos

  • INFINITE SERIES

    MODERN PUBLICATION|Exercise EXAMPLE|10 Videos

Similar Questions

Explore conceptually related problems

The points with coordinates (2a,3a), (3b,2b) and (c,c) are collinear

Prove that the points (a ,b+c),(b ,c+a)a n d(c ,a+b) are collinear.

Show that points : A (a,b+c),B(b,c+a),C(c,a+b) are collinear.

Show that points A(a,b+c),B(b,c+a) ਅਤੇ C(c,a+b) are collinear.

In any triangle ABC, prove that : a (b cos C-c cos B) = b^2 -c^2 .

If a, b, c are in A.P., prove that : (b+c)^2-a^2, (c+a)^2-b^2, (a+b)^2-c^2 are also in A.P.

If a, b, c are in A.P., prove that : a^3+4b^3+c^3=3b (a^2+c^2) .

MODERN PUBLICATION-CONIC SECTIONS-EXERCISE
  1. Find the centre, eccentricity, foci and directrices of the hyperbola ...

    Text Solution

    |

  2. Show that the triangle, the co-ordinates of whose vertices are given b...

    Text Solution

    |

  3. If a ne b ne c, prove that (a, a^2), (b, b^2), (c, c^2) can never be c...

    Text Solution

    |

  4. The vertices of a triangle ABC are A(3, 0), B(0, 6) and C(6, 9). A lin...

    Text Solution

    |

  5. A and A’ be the points (5, 0) and (-5, 0) respectively. Find the equat...

    Text Solution

    |

  6. The extremities of the base of an isosceles triangle are the points (2...

    Text Solution

    |

  7. A line is such that its segment between the straight line 5x-y-4=0 and...

    Text Solution

    |

  8. Find the distance of the line 4x - y = 0 from the point P (4, 1) measu...

    Text Solution

    |

  9. Prove that the st. line ax + by + c = 0 divides the join of (x1, y1) a...

    Text Solution

    |

  10. Prove that (-1, 4) is the orthocentre of the triangle formed by the li...

    Text Solution

    |

  11. The equation of the perpendicular bisector of the side AB of a triangl...

    Text Solution

    |

  12. Let the opposite angular points of a square be (3, 4) and (1, -1). Fin...

    Text Solution

    |

  13. Using the concept of slope, prove that medians of an equilateral trian...

    Text Solution

    |

  14. Show that the perpendicular drawn from the point (4, 1) on the line se...

    Text Solution

    |

  15. A rectangle has opposite vertices at the points (1,2) and (5, 5). If t...

    Text Solution

    |

  16. Find the centroid, incentre, circumcentre and orthocentre of the trian...

    Text Solution

    |

  17. The vertices of a triangle are : P(x1,x1 tan theta1),Q (x2, x2tantheta...

    Text Solution

    |

  18. The points (1, 3) and (5, 1) are the opposite vertices of a rectangle....

    Text Solution

    |

  19. One side of a rectangle lies along the line 4x + 7y +5=0. Two of its v...

    Text Solution

    |

  20. The consecutive sides of a parallelogram are 4x + 5y = 0 and 7x + 2y =...

    Text Solution

    |