Home
Class 12
MATHS
Let P(at^(2),2at),Q,R(ar^(2),2ar) be thr...

Let `P(at^(2),2at),Q,R(ar^(2),2ar)` be three points on a parabola `y^(2)=4ax`. If PQ is the focal chord and PK, QR are parallel where the coordinates of k is (2a,0), then the value of r is

A

`(t)/(1-t^(2))`

B

`(1-t^(2))/(t)`

C

`(t^(2)+1)/(t)`

D

`(t^(2)-1)/(t)`

Text Solution

Verified by Experts

The correct Answer is:
A, B
Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise HS (XI) AND WBJEE 2019 (HS (XI) 2019) (GROUP -A)|10 Videos

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise HS (XI) AND WBJEE 2019 (HS (XI) 2019) (GROUP -B)|14 Videos

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise HS (XI) AND WBJEE 2018 (GROUP - D)|9 Videos

  • METHOD OF SUBSTITUTION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion-Reason Type)|2 Videos

  • ORDER AND DEGREE OF DIFFERENTIAL EQUATION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (E Assertion - Reasion Type )|2 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 a, r, s, t be non-zero real numbers. Let P(at^2, 2at), Q, R(ar^2, 2ar) and S(as^2, 2as) be distinct points onthe parabola y^2 = 4ax . Suppose that PQ is the focal chord and lines QR and PK are parallel, where K isthe point (2a, 0). The value of r is

P,Q and R three points on the parabola y^(2)=4ax . If Pq passes through the focus and PR is perpendicular to the axis of the parabola, show that the locus of the mid point of QR is y^(2)=2a(x+a) .

Let A(x_(1),y_(1)) and B(x_(2),y_(2)) be two points on the parabola y^(2) = 4ax . If the circle with chord AB as a dimater touches the parabola, then |y_(1)-y_(2)| is equal to

P(alpha,alpha) is a point on the parabola y^(2)=4ax . Show that the normal chord of the parabola at P subtends a right angle at its focus.

If focal distance of a point P on the parabola y^(2)=4ax whose abscissa is 5 10, then find the value of a.

Let A(3, 0) and B(4, 1) are two points on the parabola y=(x-3)^(2) , find a point on this parabola where its tangent is parallel to the chord AB.

If the coordinates of one end of a focal chord of the parabola y^(2)=-8 be (-8, -8), then the coordinates of other end are-

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 PQ is the focal chord of parabola y=x^(2)-2x+3 such that P-=(2,3) , then find slope of tangent at Q.

CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-WBJEE 2018
  1. If sin6theta+sin4theta+sin2theta=0, then general value of theta is

    Text Solution

    |

  2. Without changing the direction of the axes, the origin is transferred ...

    Text Solution

    |

  3. The point Q is the image of the point P(1,5) about the line y=x and R ...

    Text Solution

    |

  4. The angular points of a triangle are A(-1,-7),B(5,1)andC(1,4). The equ...

    Text Solution

    |

  5. If one of the diameters of the circle, given by the equation x^(2)+y^(...

    Text Solution

    |

  6. A chord AB is drawn from the point A(0,3) on the circle x^(2)+4x+(y-3)...

    Text Solution

    |

  7. Let the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))...

    Text Solution

    |

  8. Let A, B be two distinct points on the parabola y^(2)=4x. If the axis ...

    Text Solution

    |

  9. Let P(at^(2),2at),Q,R(ar^(2),2ar) be three points on a parabola y^(2)=...

    Text Solution

    |

  10. Let P be a point on the ellipse (x^(2))/(9)+(y^(2))/(4)=1 and the line...

    Text Solution

    |

  11. Let z(1)andz(2) be complex numbers such that z(1)nez(2)and|z(1)|=|z(2)...

    Text Solution

    |

  12. From a collection of 20 consecutive natural numbers, four are selected...

    Text Solution

    |

  13. A line cuts the x-axis at A(5,0) and the y-axis at B(0,-3). A variable...

    Text Solution

    |

  14. Let A be the centre of the circle x^(2)+y^(2)-2x-4y-20=0. Let B(1,7) a...

    Text Solution

    |

  15. Consider the parabola y^(2)=4x. Let P and Q be points on the parabola ...

    Text Solution

    |

  16. If the equation x^(2)-cx+d=0 has roots equal to the fourth powers of t...

    Text Solution

    |

  17. On the occasion of Dipawali festival each student of a class sends gre...

    Text Solution

    |

  18. The area of the triangle formed by the intersectionf of a line paralla...

    Text Solution

    |

  19. A hyperbola, having the transverse axis of length 2sintheta is confoca...

    Text Solution

    |

  20. Consider the function y=log(a)(x+sqrt(x^(2)+1)),agt0,ane1. The inverse...

    Text Solution

    |