Home
Class 12
MATHS
A chord of parabola y^2=4ax subtends a r...

A chord of parabola `y^2=4ax` subtends a right angle at the vertex. Find the locus of the point of intersection of tangents at its extremities.

Text Solution

Verified by Experts

`(a^(6))/(x^(2)) + (b^(6))/(y^(2)) = (a^(2) -b^(2))^(2)`
Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION - J ( Aakash Challengers Questions )|16 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION - H ( Multiple True-False Type Questions )|5 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise section-J (Aakash Challengers Qestions)|13 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE ENGLISH|Exercise section - J|6 Videos

Similar Questions

Explore conceptually related problems

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

If a chord PQ of the parabola y^2 = 4ax subtends a right angle at the vertex, show that the locus of the point of intersection of the normals at P and Q is y^2 = 16a(x - 6a) .

If the normals drawn at the end points of a variable chord PQ of the parabola y^2 = 4ax intersect at parabola, then the locus of the point of intersection of the tangent drawn at the points P and Q is

Chords of the hyperbola x^2/a^2-y^2/b^2=1 are tangents to the circle drawn on the line joining the foci asdiameter. Find the locus of the point of intersection of tangents at the extremities of the chords.

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

Two tangents to the parabola y^2=4ax make supplementary angles with the x-axis. Then the locus of their point of intersection is

If a tangent to the parabola y^2 = 4ax intersects the x^2/a^2+y^2/b^2= 1 at A and B , then the locus of the point of intersection of tangents at A and B to the ellipse is

Statement-1: The tangents at the extremities of a focal chord of the parabola y^(2)=4ax intersect on the line x + a = 0. Statement-2: The locus of the point of intersection of perpendicular tangents to the parabola is its directrix

Find the locus of the midpoint of normal chord of parabola y^2=4ax

Chord of the parabola y^2+4y=(4)/(3)x-(16)/(3) which subtend right angle at the vertex pass through:

AAKASH INSTITUTE ENGLISH-CONIC SECTIONS-SECTION -I ( Subjective Type Questions )
  1. Two circles are inscribed and circumscribed about a square ABCD, lengt...

    Text Solution

    |

  2. The square of the length of the tangent drawn from any point on the ci...

    Text Solution

    |

  3. l and m are the lengths of the tangents from the origin and the point ...

    Text Solution

    |

  4. The least distance between two points P and Q on the circle x^(2) + y^...

    Text Solution

    |

  5. The sum of the square of the length of the chord intercepted by the li...

    Text Solution

    |

  6. The area of the region bounded by the curves {(x,y) : x^(2) + y^(2) le...

    Text Solution

    |

  7. The chord of contact of tangents from 3 points A, B, C to the circle x...

    Text Solution

    |

  8. Let x, y be real variable satisfying x^(2) + y^(2) + 8x - 10y - 59 = 0...

    Text Solution

    |

  9. If the tangent at P to the parabola y^(2) =7x is parallel to 6y -x + 1...

    Text Solution

    |

  10. Find the equation of common tangent of y^(2)=4axandx^(2)=4by.

    Text Solution

    |

  11. The mirror image of the parabola y^(2)=4x in the tangent to the parabo...

    Text Solution

    |

  12. Locus of the point of intersection of the tangents to (x^(2))/((73)^(2...

    Text Solution

    |

  13. Find the equation of the circle passing through the points of intersec...

    Text Solution

    |

  14. find the equation of parabola which is symmetric about y-axis,and pass...

    Text Solution

    |

  15. Find the point on the curve 3x^2-4y^2=72 which is nearest to the line ...

    Text Solution

    |

  16. The line passing through the extremity A of the major exis and extremi...

    Text Solution

    |

  17. If the tangents and normal to an ellipse 9x^(2) + 16y^(2) = 144 at a p...

    Text Solution

    |

  18. A chord of parabola y^2=4ax subtends a right angle at the vertex. Find...

    Text Solution

    |

  19. Let PN be the ordinate of a point P on the hyperbola x^2/(97)^2-y^2...

    Text Solution

    |

  20. Let C be a curve which is the locus of the point of intersection of li...

    Text Solution

    |