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

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|Exercise Exercise (Multiple)|26 Videos

  • PARABOLA

    CENGAGE|Exercise Exercise (Comprehension)|41 Videos

  • PARABOLA

    CENGAGE|Exercise Exercise 5.7|9 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise (Numerical)|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE|Exercise Question Bank|4 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.

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 length of a focal chord of the parabola y^2=4a x at a distance b from the vertex is c , then prove that b^2c=4a^3dot

Column I, Column II An ellipse passing through the origin has its foci (3, 4) and (6,8). Then the length of its minor axis is, p. 8 If P Q is a focal chord of the ellipse (x^2)/(25)+(y^2)/(16)=1 which passes through S-=(3,0) and P S=2, then the length of chord P Q is, q. 10sqrt(2) If the line y=x+K touches the ellipse 9x^2+16 y^2=144 , then the difference of values of K is, r. 10 The sum of distances of a point on the ellipse (x^2)/9+(y^2)/(16)=1 from the foci is, s. 12

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 the length of the common chord of two circles x^2+y^2+8x+1=0 and x^2+y^2+2muy-1=0 is 2sqrt(6) , then the values of mu are (a) +-2 (b) +-3 (c) +-4 (d) none of these

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

If S_1a n dS_2 are the foci of the hyperbola whose length of the transverse axis is 4 and that of the conjugate axis is 6, and S_3a n dS_4 are the foci of the conjugate hyperbola, then the area of quadrilateral S_1S_3S_2S_4 is 24 (b) 26 (c) 22 (d) none of these

If A B is a focal chord of x^2-2x+y-2=0 whose focus is S and A S=l_1, then find B Sdot

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

CENGAGE-PARABOLA-Exercise (Single)
  1. Two parabolas have the same focus. If their directrices are the x- and...

    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 aa n dc are the lengths of segments of any focal chord of the parab...

    Text Solution

    |

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

    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 c1a n dc2 are variable,...

    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 locus of the center of a circle which cuts orthogonally the parabo...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. The tangent to y^(2)=ax make angles theta(1)andtheta(2) with the x-axi...

    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

    |