Home
Class 11
MATHS
t 1 and  t 2 are two p...

t 1 and  t 2 are two points on the parabola `y^2 =4ax` . If the focal chord joining them coincides with the normal chord, then ` (a) t1(t1+t2)+2=0 (b)` t1+t2=0 ` (c)`` t1*t2=-1` (d) none of these     

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

The point of intersection of the tangents to the parabola y^(2)=4ax at the points t_(1) and t_(2) is -

If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2, then x^3y (dy)/(dx)= (a) 0 (b) 1 (c) -1 (d) none of these

The slope of the normal to rectangular hyperbopla xy= 4 at (2t,2/t) is a) - t^2 b) t^2 c) 2t d)-2t

If t_1a n dt_2 are the ends of a focal chord of the parabola y^2=4a x , then prove that the roots of the equation t_1x^2+a x+t_2=0 are real.

If the normal to the parabola y^2=4a x at point t_1 cuts the parabola again at point t_2 , then prove that t_2^2 geq8.

P(t_1) and Q(t_2) are the point t_1a n dt_2 on the parabola y^2=4a x . The normals at Pa n dQ meet on the parabola. Show that the middle point P Q lies on the parabola y^2=2a(x+2a)dot

If (at^(2) , 2at ) be the coordinates of an extremity of a focal chord of the parabola y^(2) = 4ax , then show that the length of the chord is a(t+(1)/(t))^(2) .

Let {t_n} be a sequence of integers in G.P. in which t_4: t_6=1:4 and t_2+t_5=216. Then t_1 is (a). 12 (b). 14 (c). 16 (d). none of these

The equation of straight line passing through (-a ,0) and making a triangle with the axes of area T is (a) 2T x+a^2y+2a T=0 (b) 2T x-a^2y+2a T=0 (c) 2T x-a^2y-2a T=0 (d)none of these

The parametric equation of a parabola is x=t^2+1,y=2t+1. Then find the equation of the directrix.

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. The endpoints of two normal chords of a parabola are concyclic. Then ...

    Text Solution

    |

  2. In parabola y^2=4x, From the point (15,12), three normals are drawn th...

    Text Solution

    |

  3. t 1 and  t 2 are two points on the parabola y^...

    Text Solution

    |

  4. Tangent and normal are drawn at the point P-=(16 ,16) of the parabola ...

    Text Solution

    |

  5. Length of the shortest normal chord of the parabola y^2=4ax is

    Text Solution

    |

  6. The line x-y=1 intersect the parabola y^(2)=4x at A and B. Normals at ...

    Text Solution

    |

  7. If normals drawn from a point P(h,k) to the parabola y^(2)=4ax, then t...

    Text Solution

    |

  8. If x+y=k is normal to y^2=12 x , then k is (a)3 (b) 9 (c) -9 (d) -3

    Text Solution

    |

  9. An equilateral triangle is inscribed in the parabola y^(2)=4ax, such...

    Text Solution

    |

  10. Evaluate, min[(x1-x2)^2+(5+sqrt(1-x1^2)-sqrt(4x2))^2],AAx1,x2 in R , ...

    Text Solution

    |

  11. The equation of the directrix of the parabola y^2+4y+4x+2=0 is (a)x=-1...

    Text Solution

    |

  12. The equation of the common tangent touching the circle (x-3)^2+y^2=9 ...

    Text Solution

    |

  13. At what point on the parabola y^2=4x the normal makes equal angle with...

    Text Solution

    |

  14. The focal chord of y^(2)=16x is tangent to (x-6)^(2)+y^(2)=2. Then t...

    Text Solution

    |

  15. The locus of the midpoint of the segment joining the focus to a moving...

    Text Solution

    |

  16. Show that the curve whose parametric coordinates are x=t^(2)+t+l,y=t^(...

    Text Solution

    |

  17. Statement 1: The line y=x+2a touches the parabola y^2=4a(x+a) Stateme...

    Text Solution

    |

  18. Consider a circle with its centre lying on the focus of the parabola, ...

    Text Solution

    |

  19. Normal drawn to y^2=4a x at the points where it is intersected by the...

    Text Solution

    |

  20. The radius of the circle touching the parabola y^2=x at (1, 1) and hav...

    Text Solution

    |