Home
Class 11
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`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 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

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. A line L passing through the focus of the parabola y^2=4(x-1) intersec...

    Text Solution

    |

  2. The ration in which the line segement joining the points (4,-6) and (...

    Text Solution

    |

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

    Text Solution

    |

  4. A water jet from a function reaches it maximum height of 4 m at a d...

    Text Solution

    |

  5. The vertex of the parabola whose parametric equation is x=t^2-t+1,y=t^...

    Text Solution

    |

  6. A point P(x , y) moves in the xy-plane such that x=acos^2theta and y=2...

    Text Solution

    |

  7. The locus of the point (sqrt(3h),sqrt(3k+2)) if it lies on the line x-...

    Text Solution

    |

  8. If the segment intercepted by the parabola y^2=4a x with the line l x+...

    Text Solution

    |

  9. The graph of the curve x^2+y^2-2x y-8x-8y+32=0 falls wholly in the fir...

    Text Solution

    |

  10. Consider two curves C1:y^2=4x ; C2=x^2+y^2-6x+1=0. Then, a. C1 and C2 ...

    Text Solution

    |

  11. Let the curve C be the mirror image of the parabola y^2 = 4x with resp...

    Text Solution

    |

  12. Let S be the focus of the parabola y^2=8x and let PQ be the common cho...

    Text Solution

    |

  13. Consider the parabola y^2 = 8x. Let Delta1 be the area of the triangle...

    Text Solution

    |

  14. Statement 1 : The curve y=-(x^2)/2+x+1 is symmetric with respect to th...

    Text Solution

    |

  15. A line L : y = mx + 3 meets y-axis at E (0, 3) and the arc of the para...

    Text Solution

    |

  16. Match the following. Normals are drawn at points P Q and R lying on th...

    Text Solution

    |

  17. Tangents and normal drawn to the parabola y^2=4a x at point P(a t^2,2a...

    Text Solution

    |

  18. If the normals to the parabola y^2=4a x at three points (a p^2,2a p) a...

    Text Solution

    |

  19. Normal AO,AA(1),andAA(2) are drawn to the parabola y^(2)=8x from the p...

    Text Solution

    |

  20. If 2x+y+lambda=0 is a normal to the parabola y^2=-8x , then lambda is ...

    Text Solution

    |