Home
Class 12
MATHS
If two distinct chords of a parabola y^2...

If two distinct chords of a parabola `y^2=4ax` , passing through (a,2a) are bisected by the line x+y=1 ,then length of latus rectum can be

A

2

B

1

C

4

D

3

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
1,2,4
Any point on x+y=1 can be taken as (t,1-t).
The equation of chord with this as midpoint is
`y(1-t)-2a(x+t)=(1-t)^(2)-4at`
It passes through (a,2a). So,
`t^(2)-2t+2a^(2)-2a+1=0`
This should have two distinct real roots. So,
Discriminant `gt0i.e.,a^(2)-alt0`
`0ltaltor0lt4alt4`
So, length of latua rectum lies in (0,4)
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE|Exercise Exercise (Comprehension)|41 Videos

  • PARABOLA

    CENGAGE|Exercise Exercise (Matrix)|4 Videos

  • PARABOLA

    CENGAGE|Exercise Exercise (Single)|98 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise (Numerical)|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE|Exercise Question Bank|19 Videos

Similar Questions

Explore conceptually related problems

If two distinct chords of a parabola y^(2)=4ax , passing through (a, 2a) are bisected on the line x + y = 1, then length of the latus-rectum can be

If two distinct chords of the parabola y ^(2) = 4ax, passing through (a, 2a) are bisected on the line x + y=1, then length of the latus-rectum can be

[" If two distinct chord of a parabola " y^(2)=4ax " passing through the point " (a,2a) " are bisected by the line " x+y=1 " then the length of the latus rectum cannot be

If 2 distinct chords of y^(2)=4ax through (a,2a) are bisected by x+y=1 then a in (0,1) (1,2) (2,3) (3,4)

If the line y=x-1 bisects two chords of the parabola y^(2)=4bx which are passing through the point (b, -2b) , then the length of the latus rectum can be equal to

If the parabola y^(2)=4ax passes through the point (3,2) then find the length of its latus rectum.

Find the condition on a and b for which two distinct chords of the hyperbola (x^(2))/(2a^(2))-(y^(2))/(2b^(2))=1 passing through (a,b) are bisected by the line x+y=b .

If the parabola y^(2)=4ax passes through the (4,-8) then find the length of latus rectum and the co-ordinates of focus.

If the set of 'K' for which two distinct chords of the ellipse (x^(2))/8+(y^(2))/2=1 passing through (2,-1) are bisected by the line x+y=K is [a,b] then (a+b) is…………

CENGAGE-PARABOLA-Exercise (Multiple)
  1. The locus of the midpoint of the focal distance of a variable point ...

    Text Solution

    |

  2. A square has one vertex at the vertex of the parabola y^2=4a x and the...

    Text Solution

    |

  3. If two distinct chords of a parabola y^2=4ax , passing through (a,2a) ...

    Text Solution

    |

  4. Let PQ be a chord of the parabola y^2=4x. A circle drawn with PQ as a...

    Text Solution

    |

  5. If the parabola x^2=ay makes an intercept of length sqrt40 unit on the...

    Text Solution

    |

  6. The equation of the directrix of the parabola with vertex at the origi...

    Text Solution

    |

  7. Tangent is drawn at any point (x1, y1) other than the vertex on the pa...

    Text Solution

    |

  8. The parabola y^2=4x and the circle having its center at 6, 5) intersec...

    Text Solution

    |

  9. Which of the following line can be tangent to the parabola y^2=8x ? x...

    Text Solution

    |

  10. If the line k^(2)(x-1)+k(y-2)+1=0 touches the parabola y^(2)-4x-4y+8=0...

    Text Solution

    |

  11. The equation of the line that touches the curves y=x|x| and x^2+(y^2-2...

    Text Solution

    |

  12. The equations of the common tangents to the parabola y = x^2 and y=-...

    Text Solution

    |

  13. The line x+ y +2=0 is a tangent to a parabola at point A, intersect t...

    Text Solution

    |

  14. Which of the following line can be normal to parabola y^2=12 x ? x+y-...

    Text Solution

    |

  15. A normal drawn to the parabola =4a x meets the curve again at Q such t...

    Text Solution

    |

  16. A circle is drawn having centre at C (0,2) and passing through focus ...

    Text Solution

    |

  17. From any point P on the parabola y^(2)=4ax, perpebdicular PN is drawn ...

    Text Solution

    |

  18. Let C1 and C2 be parabolas x^2 = y - 1 and y^2 = x-1 respectively. Let...

    Text Solution

    |

  19. The value(s) of a for which two curves y=ax^(2)+ax+(1)/(24)andx=ay^(2)...

    Text Solution

    |

  20. From any point P on the parabola y^(2)=4ax, perpebdicular PN is drawn ...

    Text Solution

    |