Home
Class 11
MATHS
The coordinates of the ends of a focal c...

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` .

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

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

The length of the common chord of the parabolas y^(2)=x and x^(2)=y is

The co-ordinates of end points of a focal chord of an ellipse are (x_1,y_1) and (x_2,y_2) .Prove that y_1y_2+4x_1x_2=0

The coordinates of the vertex of the parabola (x + 1)^(2) =- 9(y +2) are

Find the focus of the parabola y=x^2+x+1 .

If (x+1, y-2)=(3,1), find the values of x and y.

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 focal chord of the parabola y^2=a x is 2x-y-8=0 . Then find the equation of the directrix.

If (x+y,y-2) = (3,1), find the values of x and y.

If (2,-8) is at an end of a focal chord of the parabola y^2=32 x , then find the other end of the chord.

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. If y=x+2 is normal to the parabola y^(2)=4ax, then find the value of a...

    Text Solution

    |

  2. Find the equations of normals to the parabola y^(2)=4ax at the ends of...

    Text Solution

    |

  3. The coordinates of the ends of a focal chord of the parabola y^2=4a x ...

    Text Solution

    |

  4. If t(1)andt(2) are the parameter of the ends of the focal chord y^(2)=...

    Text Solution

    |

  5. If the length of focal chord of y^(2)=4ax is l, then find the angle be...

    Text Solution

    |

  6. If the length of focal PQ is 'l', and 'p' is the perpendicular distan...

    Text Solution

    |

  7. Find the equation of the tangent to the parabola y^(2)=8x having slope...

    Text Solution

    |

  8. Find the equations of the tangents of the parabola y^(2)=12x, which pa...

    Text Solution

    |

  9. If line y=3x+c touches the parabola y^(2)=12 at point P, then find the...

    Text Solution

    |

  10. Find the equation of the tangent to the parabola y=x^(2)-2x+3 at point...

    Text Solution

    |

  11. Find the equation of the tangent to the parabola x=y^(2)+3y+2 having s...

    Text Solution

    |

  12. Find the equation of tangents drawn to the parabola y=x^(2)-3x+2 from ...

    Text Solution

    |

  13. If a tangent to the parabola y^(2)=4ax meets the x-axis at T and inter...

    Text Solution

    |

  14. The parabola y^2=4x and the circle having its center at (6, 5) interse...

    Text Solution

    |

  15. The tangents to the parabola y^(2)=4ax at the vertex V and any point P...

    Text Solution

    |

  16. Show that xcosalpha+ysinalpha=p touches the parabola y^2=4a x if pcosa...

    Text Solution

    |

  17. A tangent to the parabola y^(2)=8x makes an angle of 45^(@) with the s...

    Text Solution

    |

  18. Find the equation of the common tangent of y^2=4a x and x^2=4a y.

    Text Solution

    |

  19. If the lines L(1)andL(2) are tangents to 4x^(2)-4x-24y+49=0 and are no...

    Text Solution

    |

  20. Find the shortest distance between the line y=x-2 and the parabola y=x...

    Text Solution

    |