Home
Class 12
MATHS
Length of the focal chord of the parabol...

Length of the focal chord of the parabola `(y +3)^(2) = -8(x-1)` which lies at a distance 2 units from the vertex of the parabola is

A

8

B

`6sqrt(2)`

C

9

D

`5sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
A

Lengths are invariant under change of axes. Consider `y^(2) = 8x`.
Focus is (2,0). So, focal chord at distance "2" than vertex is latus rectum which has length "8".
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE|Exercise Multiple Correct Answers Type|10 Videos
  • PARABOLA

    CENGAGE|Exercise Comprehension Type|1 Videos
  • PARABOLA

    CENGAGE|Exercise JEE Advenced Single Answer Type|18 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

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

Find the locus of the middle points of the chords of the parabola y^2=4a x which subtend a right angle at the vertex of the parabola.

The vertex of the parabola x^(2)=8y-1 is :

Find the locus of the middle points of all chords of (x^2)/4+(y^2)/9=1 which are at a distance of 2 units from the vertex of parabola y^2=-8a xdot

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

The vertex of the parabola y^2 + 4x = 0 is

Find the vertex of the parabola x^2=2(2x+y)

The vertex of the parabola y^2 = 4x + 4y is

If AFB is a focal chord of the parabola y^(2) = 4ax such that AF = 4 and FB = 5 then the latus-rectum of the parabola is equal to

The equation of the directrix of the parabola y^(2)=-8x is

CENGAGE-PARABOLA-Single Correct Answer Type
  1. If the point (2a,a) lies inside the parabola x^(2) -2x - 4y +3 = 0, th...

    Text Solution

    |

  2. If AFB is a focal chord of the parabola y^(2) = 4ax such that AF = 4 a...

    Text Solution

    |

  3. Length of the focal chord of the parabola (y +3)^(2) = -8(x-1) which l...

    Text Solution

    |

  4. Let A (0,2),B and C be points on parabola y^(2)+x +4 such that /CBA (...

    Text Solution

    |

  5. lx +my = 1 is the equation of the chord PQ of y^(2) = 4x whose focus i...

    Text Solution

    |

  6. A line from (-1,0) intersects the parabola x^(2)= 4y at A and B. Then ...

    Text Solution

    |

  7. All the three vertices of an equilateral triangle lie on the parabola ...

    Text Solution

    |

  8. Find the equations of the chords of the parabola y^2= 4ax which pass t...

    Text Solution

    |

  9. Two equal circles of largest radii have following property: (i) They...

    Text Solution

    |

  10. A and B are two points on the parabola y^(2) = 4ax with vertex O. if O...

    Text Solution

    |

  11. A line ax +by +c = 0 through the point A(-2,0) intersects the curve y^...

    Text Solution

    |

  12. Suppose a parabola y = x^(2) - ax-1 intersects the coordinate axes at ...

    Text Solution

    |

  13. The line x - b +lambda y = 0 cuts the parabola y^(2) = 4ax (a gt 0) at...

    Text Solution

    |

  14. If the parabola y=(a-b)x^2+(b-c)x+(c-a) touches x- axis then the line...

    Text Solution

    |

  15. A normal to parabola, whose inclination is 30^(@), cuts it again at an...

    Text Solution

    |

  16. If (-2,5) and (3,7) are the points of intersection of the tangent and ...

    Text Solution

    |

  17. The angle of intersection between the curves x^(2) = 4(y +1) and x^(2)...

    Text Solution

    |

  18. The parabolas y^2=4ac and x^2=4by intersect orthogonally at point P(x1...

    Text Solution

    |

  19. Sum of slopes of common tangent to y = (x^(2))/(4) - 3x +10 and y = 2 ...

    Text Solution

    |

  20. The slope of normal to be parabola y = (x^(2))/(4) -2 drawn through th...

    Text Solution

    |