Home
Class 12
MATHS
If P S Q is a focal chord of the parabol...

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

A

6

B

4

C

3

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
(3) Since the semi-latus rectum of a parabola is the harmonic mean between the segments of any focal chord of the parabola, SP, 4,SQ are in H.P. Therefore,
`4=(2SPxxSQ)/(SP+SQ)`
`or4=(2(6)(SQ))/(6+SQ)`
`or24+4(SQ)=12(SQ)`
`orSQ=3`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE PUBLICATION|Exercise EXERCISE (MULTIPLE CORRECT ANSWER TYPE )|26 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise LINKED COMPREHENSION TYPE|45 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Concept Applications Exercise 5.7|9 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 PQ is the focal chord of parabola y=x^(2)-2x+3 such that P-=(2,3) , then find slope of tangent at Q.

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-

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

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.

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

Length of the focal chord of the parabola y^2=4ax at a distance p from the vertex is:

The focal chord of the parabola y^2=a x is 2x-y-8=0 . Then find the equation of the directrix.

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 a point lying on the line y = 2x + a, a > 0 . Length of chord PQ is

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=

CENGAGE PUBLICATION-PARABOLA-EXERCISE (SINGLE CORRECT ANSWER TYPE )
  1. Two parabola have the same focus. If their directrices are the x-and t...

    Text Solution

    |

  2. PSQ is a focal chord of a parabola whose focus is S and vertex is A. P...

    Text Solution

    |

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

    Text Solution

    |

  4. The triangle P Q R of area A is inscribed in the parabola y^2=4a x suc...

    Text Solution

    |

  5. If A1B1 and A2B2 are two focal chords of the parabola y^2=4a x , then ...

    Text Solution

    |

  6. If a and c are the lengths of segments of any focal chord of the parab...

    Text Solution

    |

  7. If y=m x+c touches the parabola y^2=4a(x+a), then (a)c=a/m (b) c=a m...

    Text Solution

    |

  8. The area of the triangle formed by the tangent and the normal to the ...

    Text Solution

    |

  9. Parabola y^2=4a(x-c1) and x^2=4a(y-c2) where c1 and c2 are variables, ...

    Text Solution

    |

  10. Let y=f(x) be a parabola, having its axis parallel to the y-axis, whic...

    Text Solution

    |

  11. If y=2x-3 is tangent to the parabola y^2=4a(x-1/3), then a is equal to...

    Text Solution

    |

  12. The center of the circle which cuts parabola orthogonally the parabol...

    Text Solution

    |

  13. If the curve y=a x^2-6x+b pass through (0,2) and has its tangent paral...

    Text Solution

    |

  14. Double ordinate A B of the parabola y^2=4a x subtends an angle pi/2 at...

    Text Solution

    |

  15. find the equation of hyperabola where foci are (0,12) and (0,-12)and t...

    Text Solution

    |

  16. A tangent is drawn to the parabola y^2=4 x at the point P whose abscis...

    Text Solution

    |

  17. The straight lines joining any point P on the parabola y^2=4a x to the...

    Text Solution

    |

  18. Through the vertex O of the parabola y^2=4a x , two chords O Pa n dO Q...

    Text Solution

    |

  19. A B is a double ordinate of the parabola y^2=4a xdot Tangents drawn to...

    Text Solution

    |

  20. If the locus of the middle of point of contact of tangent drawn to the...

    Text Solution

    |