Home
Class 12
MATHS
PQ is any focal chord of the parabola y^...

PQ is any focal chord of the parabola `y^(2)=8`x. Then the length of PQ can never be less than _________ .

Text Solution

Verified by Experts

The correct Answer is:
8
(8) The length of focal chord having one extremity `(at^(2),2at)` is
`a(t+(1)/(t))^(2)`
`because|r+(1)/(t)|ge2`
we get `(t+(1)/(t))ge4a=8`
or Length of focal chord 8
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE PUBLICATION|Exercise ARCHIVES SINGLE CORRECT ANSWER TYPE|8 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise JEE ADVENCED SINGLE CORRECT ANSWER TYPE|2 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise MATRIX MATCH TYPE|5 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise Numberical Value Type|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE PUBLICATION|Exercise Comprehension|8 Videos

Similar Questions

Explore conceptually related problems

If P S Q is a focal chord of the parabola y^2=8x such that S P=6 , then the length of S Q is

If (at^(2) , 2at) be the coordinate of an extremity of a focal chord of the parabola y^(2) =4ax, then the length of the chord is-

If the point P(4, -2) is the one end of the focal chord PQ of the parabola y^(2)=x, then the slope of the tangent at Q, is

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

Let PQ be a focal chord of the parabola y^(2)=4ax . The tangents to the parabola at P and Q meet at point lying on the line y=2x+a,alt0 . If chord PQ subtends an angle theta at the vertex of y^(2)=4ax , then tantheta=

The length of focal chord to the parabola y^(2)=12x drawn from the point (3,6) on is __________ .

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 PQ be a focal chord of the parabola y^2 = 4ax The tangents to the parabola at P and Q meet at a point lying on the line y = 2x + a, a > 0 . Length of chord PQ is

PQ is a chord of the parabola y^(2) = 4ax . The ordinate of P is twice that of Q . Prove that the locus of the mid - point of PQ is 5y^(2) = 18 ax

If (2,-8) is at an end of a focal chord of the parabola y^2=32 x , then find the other end of the chord.

CENGAGE PUBLICATION-PARABOLA-NUMERICAL VALUE TYPE
  1. Consider the locus of center of the circle which touches the circle x^...

    Text Solution

    |

  2. If on a given base BC[B(0,0) and C(2,0)], a triangle is described such...

    Text Solution

    |

  3. PQ is any focal chord of the parabola y^(2)=8x. Then the length of PQ ...

    Text Solution

    |

  4. The length of focal chord to the parabola y^(2)=12x drawn from the poi...

    Text Solution

    |

  5. From the point (-1,2), tangent lines are to the parabola y^(2)=4x. If ...

    Text Solution

    |

  6. Line y=2x-b cuts the parabola y=x^(2)-4x at points A and B. Then the v...

    Text Solution

    |

  7. A line through the origin intersects the parabola 5y=2x^(2)-9x+10 at t...

    Text Solution

    |

  8. IF the circle (x-6)^2+y^2=r^2 and the parabola y^2=4x have maximum num...

    Text Solution

    |

  9. The slope of line which belongs to family (1+ l) x + (l-1)y + 2(1-l) =...

    Text Solution

    |

  10. If 3x+4y+k=0 represents the equation of tangent at the vertex of the ...

    Text Solution

    |

  11. Normals at (x(1),y(1)),(x(2),y(2))and(x(3),y(3)) to the parabola y^(2)...

    Text Solution

    |

  12. Foot of perpendicular from point P on the parabola y^(2)=4ax to the ax...

    Text Solution

    |

  13. Find the integrating factor of the following differential equation: x...

    Text Solution

    |

  14. Normals are drawn from a point P with slopes m1,m2 and m3 are drawn fr...

    Text Solution

    |

  15. The curve be y=x^2 whose slopeof tangent is x, so find the point of in...

    Text Solution

    |

  16. Find the point of intersection of the curves y= 2x^2-x+1 and y=3x+4 wh...

    Text Solution

    |

  17. Find the principal value of cos^(-1) (-(sqrt3)/2)

    Text Solution

    |

  18. If the normals of the parabola y^2=4x drawn at the end points of its l...

    Text Solution

    |

  19. If the length of the latus rectum rectum of the parabola 169{(x-1)^(2)...

    Text Solution

    |

  20. If the line x+y=6 is a normal to the parabola y^(2)=8x at point (a,b),...

    Text Solution

    |