Home
Class 12
MATHS
The angle between tangents to the parabo...

The angle between tangents to the parabola `y^2=4ax` at the points where it intersects with teine `x-y-a = 0` is `(a> 0)`

A

`pi//3`

B

`pi//4`

C

`pi//6`

D

`pi//2`

Text Solution

Verified by Experts

The correct Answer is:
D
(4) The coordinates of the focus of the parabola `y^(2)=4ax` are (a,0).
the line y-x-a=0 passes through this point. Therefore, it is a focal chord of the parabola. Hence, the tangent intersects at right angle.
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE PUBLICATION|Exercise EXERCISE (MULTIPLE CORRECT ANSWER TYPE )|26 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise LINKED COMPREHENSION TYPE|45 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Concept Applications Exercise 5.7|9 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise Numberical Value Type|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE PUBLICATION|Exercise Comprehension|8 Videos

Similar Questions

Explore conceptually related problems

The slope of the tangent to the parabola y^(2)=4ax at the point (at^(2), 2at) is -

The angle between the parabolas y^(2)=x and x^(2)=y at the origin is-

The angle between the tangents to the curves y=sin x and y = cos x at their point of intersection is

The point of intersection of the tangents to the parabola y^(2)=4ax at the points t_(1) and t_(2) is -

Find the angle between the tangents drawn to y^2=4x , where it is intersected by the line y=x-1.

The equation of the normal to the parabola y^(2) =4ax at the point (at^(2), 2at) is-

Find the angle at which the parabolas y^2=4x and x^2=32 y intersect.

If the line lx + my +n=0 is a tangent to the parabola y^(2)= 4ax , then-

y=x is tangent to the parabola y=ax^(2)+c . If c=2, then the point of contact is

Tangents are drawn to the parabola y^2=4a x at the point where the line l x+m y+n=0 meets this parabola. Find the point of intersection of these tangents.

CENGAGE PUBLICATION-PARABOLA-EXERCISE (SINGLE CORRECT ANSWER TYPE )
  1. From a point A(t) on the parabola y^(2)=4ax, a focal chord and a tange...

    Text Solution

    |

  2. The point of intersection of the tangents of the parabola y^2=4x drawn...

    Text Solution

    |

  3. The angle between tangents to the parabola y^2=4ax at the points where...

    Text Solution

    |

  4. y=x+2 is any tangent to the parabola y^2=8xdot The point P on this tan...

    Text Solution

    |

  5. If y=m1x+c and y=m2x+c are two tangents to the parabola y^2+4a(x+c)=0 ...

    Text Solution

    |

  6. Show that the tangents to the curve y=x^2-5x+6 at the point (2,0) and ...

    Text Solution

    |

  7. Two mutually perpendicular tangents of the parabola y^(2)=4ax meet the...

    Text Solution

    |

  8. Radius of the circle that passes through the origin and touches the ...

    Text Solution

    |

  9. The mirror image of the parabola y^2= 4x in the tangent to the parabol...

    Text Solution

    |

  10. Consider the parabola y^2=4xdot Let A-=(4,-4) and B-=(9,6) be two fixe...

    Text Solution

    |

  11. A line of slope lambda(0 < lambda < 1) touches the parabola y+3x^2=0 a...

    Text Solution

    |

  12. The tangent at any point P onthe parabola y^2=4a x intersects the y-ax...

    Text Solution

    |

  13. If P(t^2,2t),t in [0,2] , is an arbitrary point on the parabola y^2=4x...

    Text Solution

    |

  14. The minimum area of circle which touches the parabolas y=x^2+1 and y^2...

    Text Solution

    |

  15. If the tangents and normals at the extremities of a focal chord of a ...

    Text Solution

    |

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

    Text Solution

    |

  17. The line 2x+y+lamda=0 is a normal to the parabola y^(2)=8x, is lamda=

    Text Solution

    |

  18. about to only mathematics

    Text Solution

    |

  19. The equation of the line that passes through (10 ,-1) and is perpendic...

    Text Solution

    |

  20. Tangent and normal drawn to a parabola at A(a t^2,2a t),t!=0 meet the ...

    Text Solution

    |