Home
Class 11
MATHS
If the normals to the parabola y^2=4a x ...

If the normals to the parabola `y^2=4a x` at three points `(a p^2,2a p),` `(a q^2,2a q)` and `(a r^2,2a r)` are concurrent, then the common root of equations `P x^2+q x+r=0` and `a(b-c)x^2+b(c-a)x+c(a-b)=0` is

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

If p,q are odd integers, then the roots of the equation 2px^(2)+(2p+q)x+q=0 are

If p and q are the roots of the equation x^2+px+q =0, then

If a ,b ,c in R^+and 2b=a+c , then check the nature of roots of equation a x^2+2b x+c=0.

If PQ and Rs are normal chords of the parabola y^(2) = 8x and the points P,Q,R,S are concyclic, then

If p. q are odd integers. Then the roots of the equation 2px^(2)+(2p+q)x+q=0 are

If , p , q are the roots of the equation x^(2)+px+q=0 , then

If a ,b ,p ,q are non zero real numbers, then how many comman roots would two equations: 2a^2x^2-2a b x+b^2=0 and p^2x^2+2p q x+q^2=0 have?

Two roots of the equation, x^3+qx^2+11x-p =0 are 2 and 3, find (p-q)

The circle x^2+y^2=5 meets the parabola y^2=4x at P and Q . Then the length P Q is equal to (a)2 (b) 2sqrt(2) (c) 4 (d) none of these

If the roots of the equation qx^2+2px+2q=0 are real and unequal, prove that the roots of the equation (p+q)x^2+2qx+(p-q)=0 are imaginary.

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Statement 1 : The curve y=-(x^2)/2+x+1 is symmetric with respect to th...

    Text Solution

    |

  2. Tangent and normal drawn to a parabola at A(a t^2,2a t),t!=0 meet the ...

    Text Solution

    |

  3. If the normals to the parabola y^2=4a x at three points (a p^2,2a p), ...

    Text Solution

    |

  4. Normals A O ,A A1a n dA A2 are drawn to the parabola y^2=8x from the p...

    Text Solution

    |

  5. If 2x+y+lambda=0 is a normal to the parabola y^2=-8x , then lambda is ...

    Text Solution

    |

  6. The length of the latus rectum of the parabola whose focus is a. ((u...

    Text Solution

    |

  7. If parabolas y^(2)=lamdaxand25[(x-3)^(2)+(y+2)^(2)]=(3x-4y-2)^(2) are ...

    Text Solution

    |

  8. If normal to parabola y^(2)=4ax at point P(at^(2),2at) intersects the ...

    Text Solution

    |

  9. The set of points on the axis of the parabola y^2=4x+8 from which the ...

    Text Solution

    |

  10. Which one of the following equation represent parametric equation to a...

    Text Solution

    |

  11. The vertex of a parabola is the point (a , b) and the latus rectum is ...

    Text Solution

    |

  12. The curve represented by the equation sqrt(p x)+sqrt(q y)=1 where p ,q...

    Text Solution

    |

  13. Prove that the equation of the parabola whose focus is (0, 0) and tang...

    Text Solution

    |

  14. The equation of the parabola whose vertex and focus lie on the axis of...

    Text Solution

    |

  15. Prove that for a suitable point P on the axis of the parabola y^(2)=4a...

    Text Solution

    |

  16. Two parabola have the same focus. If their directrices are the x-and t...

    Text Solution

    |

  17. The number of common chord of the parabolas x=y^(2)-6y+11andy=x^(2)-6x...

    Text Solution

    |

  18. Find the equation of the curve whose parametric equations are x=1+4c...

    Text Solution

    |

  19. Prove that any point on the ellipse whose foci are (-1,0) and (7,0)...

    Text Solution

    |

  20. Find the eccentric angle of a point on the ellipse (x^2)/6+(y^2)/2=...

    Text Solution

    |