Home
Class 11
MATHS
If the extremitied of a focal chord of t...

If the extremitied of a focal chord of the parabola `y^2=4ax`be `(at_1^2,2at_1)`and `(at_2^2,2at_2)`,show that `t_1t_2=-1`

Promotional Banner

Topper's Solved these Questions

  • ANNUAL EXAMINATION QUESTION PAPERS 2015

    UNITED BOOK HOUSE|Exercise EXERCISE|49 Videos
  • ANNUAL EXAMINATION QUESTION PAPERS 2017

    UNITED BOOK HOUSE|Exercise EXERCISE|50 Videos

Similar Questions

Explore conceptually related problems

If the extremities of a focal chord of the parabola y^(2) = 4ax be (at_(1)^(2) , 2at_(1)) and (at_(2)^(2) ,2at_(2)) , show that t_(1)t_(2) = - 1

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

If athe coordinates of one end of a focal chord of the parabola y^(2) = 4ax be (at^(2) ,2at) , show that the coordinates of the other end point are ((a)/(t^(2)),(2a)/(t)) and the length of the chord is a(t+(1)/(t))^(2)

The coordinates of the ends of a focal chord of the parabola y^2=4a x are (x_1, y_1) and (x_2, y_2) . Then find the value of x_1x_2+y_1y_2 .

If the tangents and normals at the extremities of a focal chord of a parabola intersect at (x_1,y_1) and (x_2,y_2), respectively, then (a) x_1=y_2 (b) x_1=y_1 (c) y_1=y_2 (d) x_2=y_1

The locus of the middle points of the focal chords of the parabola, y^2=4x is:

If alpha and beta be the eccentric angles of the extremities of a focal chord of the hyperbola b^(2)x^(2) - a^(2)y^(2) = a^(2)b^(2) , show that, tan(alpha)/(2)tan(beta)/(2) = -(e-1)/(e+1) , (e-1)/(e+1) (e is the eccentricity of the hyperbola.).

Length of the focal chord of the parabola y^2=4ax at a distance p from the vertex is:

If (at^(2) , 2at) be the coordinate of an extremity of a focal chord of the parabola y^(2) =4ax, then the length of the chord is-

If (at^(2) , 2at ) be the coordinates of an extremity of a focal chord of the parabola y^(2) = 4ax , then show that the length of the chord is a(t+(1)/(t))^(2) .

UNITED BOOK HOUSE-ANNUAL EXAMINATION QUESTION PAPERS 2016-EXERCISE
  1. The equations of two sides of a square are 5x+12y-10=0 and 5x+12y+29=0...

    Text Solution

    |

  2. Find the equation of the circle passes through the points (4,3) and (-...

    Text Solution

    |

  3. Show that the area of the triangle formed by the lines y = m(1) x + c(...

    Text Solution

    |

  4. Find the value of cos B for the triangle formed by joining the points ...

    Text Solution

    |

  5. Evlauate lim(xrarr0)(cot2x-cosec2x)/x

    Text Solution

    |

  6. Find from the first principle,the derivative of f(x)=e^(x^2)at x=1.

    Text Solution

    |

  7. Prove the following by contradiciton ."The sum of a rational and an ir...

    Text Solution

    |

  8. Check the validity of the following compound propostions :"72 is a mul...

    Text Solution

    |

  9. Check the validity of the following compound propostions :"120 is a mu...

    Text Solution

    |

  10. Two students Anil and Ashima appeared is an examination. The probabili...

    Text Solution

    |

  11. Find the coefficient of variation of the following data:

    Text Solution

    |

  12. Find the general solution of x and y satisfying the equation 5sinx.cos...

    Text Solution

    |

  13. Find the domain of definition and range of the function f(x)=x/(1+x^2)...

    Text Solution

    |

  14. If f(x)=ax^2+bx+cand f(2)=1,f(3)=6,f(-1)=10,then find the value of f(1...

    Text Solution

    |

  15. If z=x+iy and |z-1|+|z+1|=4,then show that 3x^2+4y^2=12,where i=sqrt-1

    Text Solution

    |

  16. In how many ways can 6 boys and 4 girls be seated in a round table so ...

    Text Solution

    |

  17. If a1,a2,a3,...,anare in A.P then show that 1/(a1a2)+1/(a2a3)+1/(a3a4)...

    Text Solution

    |

  18. Solve :(|x|-2)/(|x|-3)ge0,where x in R and x!=+-3

    Text Solution

    |

  19. If the extremitied of a focal chord of the parabola y^2=4axbe (at1^2,2...

    Text Solution

    |

  20. The number of tangents that can be drawn from the point (6, 2) on the ...

    Text Solution

    |