Home
Class 12
MATHS
Prove that the portion or the tangent in...

Prove that the portion or the tangent intercepted,between the point of contact and the directrix of the parabola `y^(2)= 4ax` subtends a right angle at its focuc.

A

`30^(@)`

B

`45^(@)`

C

`60^(@)`

D

`90^(@)`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 1B|50 Videos

  • PARABOLA

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 (SPECIAL TYPE QUESTIONS ) SET-1|4 Videos

  • PARABOLA

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 (SPECIAL TYPE QUESTIONS ) SET-4|4 Videos

  • MEASURES OF DISPERSION

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE-2 ( SET -4)|2 Videos

  • PARTIAL FRACTIONS

    DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 SET - 4|2 Videos

Similar Questions

Explore conceptually related problems

The point of contact of 2x-y+2 =0 to the parabola y^(2)=4ax is

The point of contact of x-2y+4a=0 to the parabola y^(2)=4ax is

The equation of the directrix of the parabola y^(2)-4ay-2ax=0 is

If the normal chord drawn at the point P(t) to the parabola y^(2) = 4ax subtends a right angle at the focus, then show that , = pm2

If a normal chord of a puint on the parabola y^(2) = 4ax , subtends a right angle at the vertex, then t =

DIPTI PUBLICATION ( AP EAMET)-PARABOLA-EXERCISE 1 A
  1. The length of chord intercepted by the parabola y=x^(2)+3x on the line...

    Text Solution

    |

  2. If the line y = mx + a meets the parabola x^(2)=4ay in two points whos...

    Text Solution

    |

  3. Prove that the portion or the tangent intercepted,between the point of...

    Text Solution

    |

  4. The subnormal of the parabola y^(2)=4ax is equal to

    Text Solution

    |

  5. If a normal chord of a puint on the parabola y^(2) = 4ax, subtends a r...

    Text Solution

    |

  6. If the chord y = mx +c subtends a right angle at the vertex of the par...

    Text Solution

    |

  7. If P is a point on the parabola y^(2)=8x and A is the point (1,0) then...

    Text Solution

    |

  8. The locus of the point of intersection of two tangents to the parabola...

    Text Solution

    |

  9. The tangents at the points (at(1)^(2),2at(1)) , (at(2)^(2),2at(2)) on ...

    Text Solution

    |

  10. The tangent to y^(2)=ax makes an angle 45^(@) with x-axis . Then its ...

    Text Solution

    |

  11. The tangents at the points (at(1)^(2),2at(1)) , (at(2)^(2),2at(2)) on ...

    Text Solution

    |

  12. If P (at(1)^(2),2at(1)) and Q (at(2)^(2),2at(2)) are two variable poin...

    Text Solution

    |

  13. The length of the chord of contact of tangents drawn from (x(1),y(1)) ...

    Text Solution

    |

  14. The area of the triangle formed by the tangents and chord of contact f...

    Text Solution

    |

  15. If y(1),y(2) and y(3) are the ordinates of the vertices of a triangle ...

    Text Solution

    |

  16. The area of the triangle inscribed in the parabola y^(2)=4x the ordina...

    Text Solution

    |

  17. The tangents to the parabola y^(2)=4ax at P(t(1)) and Q (t(2)) inters...

    Text Solution

    |

  18. The orthocentre of the triangle formed by three tangents to the parabo...

    Text Solution

    |

  19. Prove that the orthocentre of the triangle formed by any three tangent...

    Text Solution

    |

  20. The feet of the perpendiculars drawn from the focus of a parabola to t...

    Text Solution

    |