Home
Class 11
MATHS
If the normal chord of the parabola y^(2...

If the normal chord of the parabola `y^(2)=4x` makes an angle `45^(@)` with the axis of the parabola, then its length, is

A

8

B

`8sqrt2`

C

4

D

`4sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
B
The equation of a normal to `y^(2)=4x" at "P(t^(2), 2t)` is
`y+tx=2t+t^(3)`
This makes an angle of `45^(@)` with x-axis. Therefore, t=-1. If it culs the parabola at `Q(t_(1)_^(2),2t_(1))`, then
`t_(1)=-t-2/t=3`
Thus, the coordinates of P and Q are (1, -2) and (9, 0) respectively.
`:." "PQ=sqrt(64+64)=8sqrt2`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|66 Videos

  • PARABOLA

    OBJECTIVE RD SHARMA ENGLISH|Exercise SECTION-I (SOLVED MCQs EXAMPLE)|1 Videos

  • PAIR OF STRAIGHT LINES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|18 Videos

  • PERMUTATIONS AND COMBINATIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|60 Videos

Similar Questions

Explore conceptually related problems

The length of a focal chord of the parabola y^2=4ax making an angle theta with the axis of the parabola is (a> 0) is :

A circle of radius 4 drawn on a chord of the parabola y^(2)=8x as diameter touches the axis of the parabola. Then the slope of the chord is

A normal chord of the parabola y^2=4ax subtends a right angle at the vertex if its slope is

The locus of the point of intersection of two tangents to the parabola y^(2)=4ax which make complementary angles with the axis of the parabola is

A tangent to the parabola y^(2)=16x makes an angle of 60^(@) with the x-axis. Find its point of contact.

If a normal to a parabola y^2 =4ax makes an angle phi with its axis, then it will cut the curve again at an angle

Show that the focal chord, of parabola y^2 = 4ax , that makes an angle alpha with the x-axis is of length 4a cosec^2 alpha .

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

OA is the chord of the parabola y^(2)=4x and perpendicular to OA which cuts the axis of the parabola at C. If the foot of A on the axis of the parabola is D, then the length CD is equal to

Statement 1: The length of focal chord of a parabola y^2=8x making on an angle of 60^0 with the x-axis is 32. Statement 2: The length of focal chord of a parabola y^2=4a x making an angle with the x-axis is 4acos e c^2alpha

OBJECTIVE RD SHARMA ENGLISH-PARABOLA-Chapter Test
  1. If the normal chord of the parabola y^(2)=4x makes an angle 45^(@) wit...

    Text Solution

    |

  2. If y=2x+k is a tangent to the curve x^(2)=4y, then k is equal to

    Text Solution

    |

  3. The normal drawn at a point (a t1 2,-2a t1) of the parabola y^2=4a x m...

    Text Solution

    |

  4. The mid-point of the chord 2x+y-4=0 of the parabola y^(2)=4x is

    Text Solution

    |

  5. The two ends of latusrectum of a parabola are the points (3, 6) and (-...

    Text Solution

    |

  6. Prove that the locus of the middle points of all chords of the parabol...

    Text Solution

    |

  7. The focus of the parabola x^2-8x+2y+7=0 is

    Text Solution

    |

  8. The point of contact of the line x-2y-1=0 with the parabola y^(2)=2(x-...

    Text Solution

    |

  9. Find the number of distinct normals that can be drawn from (-2,1) to t...

    Text Solution

    |

  10. At what point on the parabola y^2=4x the normal makes equal angle with...

    Text Solution

    |

  11. Three normals to the parabola y^2= x are drawn through a point (C, O) ...

    Text Solution

    |

  12. The normal chord of a parabola y^2= 4ax at the point P(x1, x1) subten...

    Text Solution

    |

  13. AB, AC are tangents to a parabola y^2=4ax; p1, p2, p3 are the lengths...

    Text Solution

    |

  14. The circles on the focal radii of a parabola as diameter touch: A) th...

    Text Solution

    |

  15. If the normals from any point to the parabola y^2=4x cut the line x=2 ...

    Text Solution

    |

  16. about to only mathematics

    Text Solution

    |

  17. The equation of the tangent to the parabola y^(2)=8x which is perpendi...

    Text Solution

    |

  18. the tangent drawn at any point P to the parabola y^2= 4ax meets the di...

    Text Solution

    |

  19. about to only mathematics

    Text Solution

    |

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

    Text Solution

    |

  21. A variable circle passes through the fixed point (2, 0) and touches y-...

    Text Solution

    |