Home
Class 12
MATHS
If (a , b) is the midpoint of a chord pa...

If `(a , b)` is the midpoint of a chord passing through the vertex of the parabola `y^2=4x ,` then (a)`a=2b` (b) `a^2=2b` (c)`a^2=2b` (d) `2a=b^2`

A

a=2b

B

2a=b

C

`a^2=2b`

D

`2a=b^2`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Option Correct Type Questions)|30 Videos

  • PARABOLA

    ARIHANT MATHS ENGLISH|Exercise Exercise (More Than One Correct Option Type Questions)|14 Videos

  • PARABOLA

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|20 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|28 Videos

Similar Questions

Explore conceptually related problems

If(a, b) is midpoint of a chord passing through the vertex of the parabola y^(2)=4x then

If (a ,b) is the midpoint of a chord passing through the vertex of the parabola y^2=4(x+1), then prove that 2(a+1)=b^2

If (a ,b) is the midpoint of a chord passing through the vertex of the parabola y^2=4(x+1), then prove that 2(a+1)=b^2 .

The vertex of the parabola y^(2) =(a-b)(x -a) is

(a) a^2+b^2 (b) a+b (c) a^2-b^2 (d) sqrt(a^2+b^2)

If a!=0 and the line 2b x+3c y+4d=0 passes through the points of intersection of the parabolas y^2=4a x and x^2=4a y , then (a) d^2+(2b+3c)^2=0 (b) d^2+(3b+2c)^2=0 (c) d^2+(2b-3c)^2=0 (d)none of these

If x=asectheta and y=btantheta , then b^2x^2-a^2y^2= (a) a b (b) a^2-b^2 (c) a^2+b^2 (d) a^2b^2

The vertex of the parabola (y-2)^2=16(x-1) is a. (1,2) b. (-1,2) c. (1,-2) d. (2,1)

The locus of the point of inter section of perpendicular chords passing through the foci of the ellipse x^2/a^2+y^2/b^2=1(a >b) is

In the parabola y^2=4a x , the length of the chord pasing through the vertex and inclined to the axis at pi//4 is a. 4sqrt(2)a b. 2sqrt(2)a c. sqrt(2)a d. none of these

ARIHANT MATHS ENGLISH-PARABOLA-Exercise For Session 2
  1. The normals at three points P,Q,R of the parabola y^2=4ax meet in (h,k...

    Text Solution

    |

  2. The set of points on the axis of the parabola y^2-4x-2y+5=0 from which...

    Text Solution

    |

  3. Prove that any three tangents to a parabola whose slopes are in harmon...

    Text Solution

    |

  4. prove that the locus of the point of intersection of the tangents at t...

    Text Solution

    |

  5. Find the equation of the normal to the parabola y^2=4x which is para...

    Text Solution

    |

  6. Find the equation of the normal to the parabola y^2=4x which is perp...

    Text Solution

    |

  7. The ordinates of points P and Q on the parabola y^2=12x are in the rat...

    Text Solution

    |

  8. The normals at P, Q, R on the parabola y^2 = 4ax meet in a point on th...

    Text Solution

    |

  9. Three normals are drawn from (2lamda,0) to the parabola y^2=4x .Show t...

    Text Solution

    |

  10. If m1,m2 are the slopes of the two tangents that are drawn from (2,3) ...

    Text Solution

    |

  11. Find the angle between the tangents drawn from the origin to the pa...

    Text Solution

    |

  12. If (a , b) is the midpoint of a chord passing through the vertex of th...

    Text Solution

    |

  13. The diameter of the parabola y^2=6x corresponding to the system of par...

    Text Solution

    |

  14. Tangents are drawn from the point (-1, 2) to the parabola y^2 =4x The ...

    Text Solution

    |

  15. for parabola x^2+y^2+2xy−6x−2y+3=0, the focus is.

    Text Solution

    |

  16. Find the locus of the middle points of the chords of the parabola y^2=...

    Text Solution

    |

  17. A ray of light moving parallel to the x-axis gets reflected form a ...

    Text Solution

    |

  18. The locus of the point of intersection of the tangents to the parabola...

    Text Solution

    |

  19. about to only mathematics

    Text Solution

    |

  20. Tangents are drawn from the point (-1, 2) to the parabola y^2 =4x The ...

    Text Solution

    |