Home
Class 11
MATHS
The parabola y^2=4ax passes through the ...

The parabola `y^2=4ax` passes through the point (2,-6). Find the length of the latus rectum.

Text Solution

Verified by Experts

`(-6)^2=4a cdot 2` (Since the parabola passes through (2,-6)
or, 36=8a `therefore a = 9/2` Hence length of L.R. = 4a=18 units
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    PATHFINDER|Exercise QUESTION BANK|67 Videos

  • DERIVATIVES

    PATHFINDER|Exercise QUESTION BANK|81 Videos

Similar Questions

Explore conceptually related problems

The parabola y^(2) =- 4ax passes through the point (-1,2) . Find the coordinates of its focus and length of latus rectum.

If normals drawn at three different point on the parabola y^(2)=4ax pass through the point (h,k), then show that hgt2a .

The parabola x^(2) +2py = 0 passes through the point (4,-2) , find the coordinates of focus and the length of latus rectum .

If the point P(at^2,2at) is a end point of a chord of the parabola y^2=4ax which is passes through the focus, then the length of the chord is

If the parabola y^(2) = 4 ax passes through the point of intersection of the straight lines 3x + y + 5 = 0 and x + 3y - 1 = 0 , find the coordinates of its focus and the length of its latus rectum .

For what value of m the hyperbola 3x^(2)-my^(2) = 48 will pass through the poin (8,-6) ? Find its eccentricity and the length of latus rectum.

If a + bne 0 , find the coordinates of focus and the length of latus rectum of the parabola y^(2) = 2 mx which passes through the point of intersection of the straight lines (x)/(a)+(y)/(b)=1 and (x)/(b)+(y)/(a)=1 .

In each of the following find the coordinates of the focus , axis of the parabola , the equation of the directrix and the length of the latus rectum. x^(2)=6y

In each of the following find the coordinates of the focus , axis of the parabola , the equation of the directrix and the length of the latus rectum. x^(2)=-16y

In each of the following find the coordinates of the focus , axis of the parabola , the equation of the directrix and the length of the latus rectum. x^(2)=-9y

PATHFINDER-CONIC SECTION-QUESTION BANK
  1. Find the equation of the circle whose centre is the points (2,-3) and ...

    Text Solution

    |

  2. Find the equation of the circle which has A(1,3) and B(4,5) as the opp...

    Text Solution

    |

  3. The parabola y^2=4ax passes through the point (2,-6). Find the length ...

    Text Solution

    |

  4. Find whether (4,-2) is on the exterior, interior or on the circle whos...

    Text Solution

    |

  5. Do the points (-2,5),(3,-4) lie on the same or opposite sides of the c...

    Text Solution

    |

  6. One end of a diameter of the circle x^2+y^2-3x+5y-4=0 is (2,1). Find t...

    Text Solution

    |

  7. Find the focus, directrix and eccentricity of the parabola y^2=2 sqrt(...

    Text Solution

    |

  8. In each of the following find the coordinates of the focus , axis of t...

    Text Solution

    |

  9. Find the locus of the point P, sum of whose distance from the points F...

    Text Solution

    |

  10. In each of the Find the coordinates of the foci, the vertices, the len...

    Text Solution

    |

  11. Find the equation of the ellipse with e=3/4, foci on y-axis, centre at...

    Text Solution

    |

  12. A rod PQ of length 16 units moves with its ends P and Q always touchin...

    Text Solution

    |

  13. Find the locus of the point P, sum of whose distances from the pointsF...

    Text Solution

    |

  14. Find the equation of a parabola whose focus is (1,2) and directrix is ...

    Text Solution

    |

  15. Find the equation of an ellipse with eccentricity 1/2, focus F(1,1) an...

    Text Solution

    |

  16. The foci of a hyperbola coincide with the foci of the ellipse x^2/25 +...

    Text Solution

    |

  17. A man running on a race course notes that the sum of his distances fro...

    Text Solution

    |

  18. An arch is in the from of a semi - ellipse. It is 8 m wide and 2 m hig...

    Text Solution

    |

  19. A parabolic reflector is 40 cm in diameter and 10 cm deep. Find the po...

    Text Solution

    |

  20. Find the equation of a circle which passes through the origin and make...

    Text Solution

    |