Home
Class 12
MATHS
If (2,-8) is at an end of a focal chord ...

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.

Text Solution

Verified by Experts

We have parabola `y^(2)=32x`.
One end of focal chord is `P(2,-8)-=P(8t^(2),16t)`.
`:." "t=-1//2`
Thus, parameter of the other end Q of the focal chord PQ is 2.
Therefore, coordinates of Q are `(8(2)^(2),16(2))-=(32, 32)`.
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE|Exercise Exercise 5.1|11 Videos

  • PARABOLA

    CENGAGE|Exercise Exercise 5.2|17 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise (Numerical)|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE|Exercise Question Bank|19 Videos

Similar Questions

Explore conceptually related problems

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

If (t^(2),2t) is one end ofa focal chord of the parabola,y^(2)=4x then the length of the focal chord will be:

The focal chord of the parabola y^(2)=ax is 2x-y-8=0. Then find the equation of the directrix.

If the point P(4, -2) is the one end of the focal chord PQ of the parabola y^(2)=x, then the slope of the tangent at Q, is

If P(2, 1) is one end of focal chord PQ of the parabola x^(2)+2y- 2x-2=0 then the slope of the normal at Q is

If P(-3, 2) is one end of the focal chord PQ of the parabola y^(2) + 4x + 4y = 0 , then the slope of the normal at Q is

CENGAGE-PARABOLA-Question Bank
  1. If (2,-8) is at an end of a focal chord of the parabola y^2=32 x , the...

    Text Solution

    |

  2. If (alpha, beta) is a point on parabola y^2=4 x which is nearest to th...

    Text Solution

    |

  3. The, focall chord of the parabola (y-2)^2=16(x-1) is a tangent to the ...

    Text Solution

    |

  4. A chord P Q is a normal to the y^2=4 a x at P and subtendsa right ang...

    Text Solution

    |

  5. If radius of circle passing through the focus of parabola x^2=4 y and ...

    Text Solution

    |

  6. The equation of latus rectum of a parabola is x+y=8 and cquation of th...

    Text Solution

    |

  7. Normals of parabola y^2=4 x at P and Q meet at R(x2, 0) and tangents a...

    Text Solution

    |

  8. Chord of the curve 3 x^2-y^2-2 x+4 y=0, which subtends a right angle a...

    Text Solution

    |

  9. If the equation lambda(4 x-3)^2+4(2 y-7)^2right=mu(4 x-3 y+3)^2 repres...

    Text Solution

    |

  10. Tangents are drawn from any point.on directrix of y^2=16 x to parabola...

    Text Solution

    |

  11. Absoulte value of y -intercept of the common tangent to the parabola y...

    Text Solution

    |

  12. Let y=x+1 be the axis of parabola, y+x-4=0 be the tangent of same para...

    Text Solution

    |

  13. Let the parabola y=a x^2+b x+c has vertex at M(4,2) and a in[1,3] . If...

    Text Solution

    |

  14. From the point (4,6), a pair of tangent lines is drawn to the parabola...

    Text Solution

    |

  15. If the normal to a parabola y^2=4 a x at P meets the curve again in Q ...

    Text Solution

    |

  16. A circle is drawn to pass through the extremities of the latus rectum ...

    Text Solution

    |

  17. If (-2,7) is the highest point on the graph of y=-2 x^2-4 a x+k, ...

    Text Solution

    |

  18. The tangent at P(1,2) to the parabola y^2=4 x meets the tangent at ver...

    Text Solution

    |

  19. If three normals are drawn from the point (6,0) to the parabola y^2=4 ...

    Text Solution

    |

  20. Square of the area of the triangle formed by end points of a focal cho...

    Text Solution

    |

  21. Let S be the set all points (x, y) satisfying y^2 le 16 x . For points...

    Text Solution

    |