Home
Class 12
MATHS
If the bisector of angle A P B , where P...

If the bisector of angle `A P B ,` where `P Aa n dP B` are the tangents to the parabola `y^2=4a x ,` is equally, inclined to the coordinate axes, then the point `P` lies on the

A

tangent at vertex of the parabola

B

directrix of the parabola

C

circle with center at the origin and radius

D

the line of latus rectum

Text Solution

Verified by Experts

The correct Answer is:
D
(4)
Here, `(1)/(t_(1))="tan"((pi)/(4)+theta)`
`and(1)/(t_(2))="tan"((pi)/(4)-theta)`
So, `t_(1)t_(2)=1`
Therefore, the x-coordinate of P is `at_(1)t_(2),i.e.,a`.
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 -

If two tangents drawn from a point P to the parabola y^2 = 4x are at right angles, then the locus of P is

T P and T Q are tangents to the parabola y^2=4a x at Pa n dQ , respectively. If the chord P Q passes through the fixed point (-a ,b), then find the locus of Tdot

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)

If the tangent at any point P to the parabola y^(2)=4ax meets the directrix at the point K , then the angle which KP subtends at its focus is-

Find the points of contact Q and R of a tangent from the point P(2,3) on the parabola y^2=4xdot

If the tangent at (1,1) on y^2=x(2-x)^2 meets the curve again at P , then find coordinates of P .

The point (8,4) lies inside the parabola y^(2) = 4ax If _

Find the locus of the point of intersection of tangents in the parabola x^2=4a xdot which are inclined at an angle theta to each other. Which intercept constant length c on the tangent at the vertex. such that the area of A B R is constant c , where Aa n dB are the points of intersection of tangents with the y-axis and R is a point of intersection of tangents.

A P is perpendicular to P B , where A is the vertex of the parabola y^2=4x and P is on the parabola. B is on the axis of the parabola. Then find the locus of the centroid of P A Bdot

CENGAGE PUBLICATION-PARABOLA-EXERCISE (SINGLE CORRECT ANSWER TYPE )
  1. A B is a double ordinate of the parabola y^2=4a xdot Tangents drawn to...

    Text Solution

    |

  2. If the locus of the middle of point of contact of tangent drawn to the...

    Text Solution

    |

  3. If the bisector of angle A P B , where P Aa n dP B are the tangents to...

    Text Solution

    |

  4. From a point A(t) on the parabola y^(2)=4ax, a focal chord and a tange...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |