Home
Class 12
MATHS
Let a, r, s, t be non-zero real numbers....

Let a, r, s, t be non-zero real numbers. Let `P(at^(2),2at),Q(ar^(2),2ar)andS(as^(2),2as)` be distinct points on the parabola `y^(2)=4ax`. Suppose that PQ is the focal chord and lines QR and PK are parallel, where K the point (2a,0).
The value of r is

A

`-1/t`

B

`(t^2+1)/t`

C

`1/t`

D

`(t^2-1)/t`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|15 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|28 Videos

Similar Questions

Explore conceptually related problems

Let a, r, s, t be non-zero real numbers. Let P(at^(2),2at),Q(ar^(2),2ar)andS(as^(2),2as) be distinct points on the parabola y^(2)=4ax . Suppose that PQ is the focal chord and lines QR and PK are parallel, where K the point (2a,0). If st=1, then the tangent at P and the normal at S to the parabola meet at a point whose ordinate is

Let PQ be a focal chord of the parabola y^(2)=4ax . The tangents to the parabola at P and Q meet at point lying on the line y=2x+a,alt0 . The length of chord PQ is

Find a point on the parabola y = (x-2)^2 , where the tangent is parallel to the chord joining (2,4) and (4,4)

Let P , Q and R are three co-normal points on the parabola y^2=4ax . Then the correct statement(s) is /at

Let a and b be non-zero real numbers. Then the equation : (ax^2 + by^2 + c)(x^2 - 5xy + 6y^2) = 0 represents :

Let (x,y) be any point on the parabola y^2= 4x . Let P be the point that divides the line segment from (0, 0) to (x, y) in the ratio 1 : 3. Then the locus of P is:

Let A and B be two distinct points on the parabola y^2=4x . If the axis of the parabola touches a circle of radius r having AB as its diameter, then find the slope of the line joining A and B .

Find a point on the parabola y = (x-3)^2 , where the tangent s parallel to the chord joining (3,0) and (4,1)

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

3 point O (0,0),P(a,a^2),Q(-b,b^2)(agt0,bgt0) are on the parabola y=x^2 . Let S_(1) be the area bounded by the line PQ and parabola let S_2 be the area of the Delta OPQ , the minimum value of S_(1)//S_(2) is

ARIHANT MATHS-PARABOLA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If two tangents drawn from a point P to the parabola y2 = 4x are at ri...

    Text Solution

    |

  2. Of the 125 students in an elementary school, 89 students play checkers...

    Text Solution

    |

  3. What is the 5th term of this sequence 9, 13, 17, ...?

    Text Solution

    |

  4. In a group of 400 people, 250 can speak Punjabi and 200 can speak Engl...

    Text Solution

    |

  5. If f (x) = a cos (bx + c) + d, then what is the range of f (x)?

    Text Solution

    |

  6. If f (x) = 3x − 5, then inverse of f(x) is

    Text Solution

    |

  7. Let PQ be a focal chord of the parabola y^(2)=4ax. The tangents to the...

    Text Solution

    |

  8. Let PQ be a focal chord of the parabola y^(2)=4ax. The tangents to the...

    Text Solution

    |

  9. The slope of the line touching both the parabolas y^2=4x and x^2=−32y ...

    Text Solution

    |

  10. Evaluate int 28x^2 dx.

    Text Solution

    |

  11. Let a, r, s, t be non-zero real numbers. Let P(at^(2),2at),Q(ar^(2),2a...

    Text Solution

    |

  12. Let a, r, s, t be non-zero real numbers. Let P(at^(2),2at),Q(ar^(2),2a...

    Text Solution

    |

  13. Let O be the vertex and Q be any point on the parabola,x^2=""8y . It...

    Text Solution

    |

  14. If the normals of the parabola y^(2)=4x drawn at the end points of its...

    Text Solution

    |

  15. Let P and Q be distinct points on the parabola y^2 = 2x such that a c...

    Text Solution

    |

  16. Let P be the point on the parabola, y^(2)=8x which is at a minimum dis...

    Text Solution

    |

  17. The circle C1 : x^2 + y^2 = 3, with center at O, intersects the parabo...

    Text Solution

    |

  18. Let P be the point on the parabola y^(2)4x which is at the shortest di...

    Text Solution

    |

  19. The radius of a circle, having minimum area, which touches the curve...

    Text Solution

    |

  20. If a chord which is not a tangent, of the parabola y^(2)=16x has the e...

    Text Solution

    |