Home
Class 12
MATHS
Statement-I If a circle S=0 intersect hy...

Statement-I If a circle S=0 intersect hyperbola `xy=4` at four points, three of them being `(2, 2), (4, 1) and (6, (2)/(3)`, then the coordinate of the fourth point are `((1)(4), 16)`.
Statement-II If a circle S=0 intersects a hyperbola `xy=c^(2)` at `t_1, t_2, t_3 and t_4`, then `t_1t_2t_3t_4=1`

A

Statement-I is true, Statement-II is also true, Statement-II is the correct explanation of Statement-I.

B

Statement-I is true, Statement-II is also true, Statement-II is not the correct explanation of Statement-I.

C

Statement-I is true, Statement-II is false.

D

Statement-I is false, Statement-II is true

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    ARIHANT MATHS|Exercise JEE Type Solved Examples : Subjective Type Questions|1 Videos

  • HYPERBOLA

    ARIHANT MATHS|Exercise Exercise For Session 1|19 Videos

  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

  • INDEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|8 Videos

Similar Questions

Explore conceptually related problems

If a circle and the rectangular hyperbola xy = c^(2) meet in four points 't'_(1) , 't'_(2) , 't'_(3) " and " 't'_(4) then prove that t_(1) t_(2) t_(3) t_(4) = 1 .

If the normal to the rectangular hyperbola xy = 4 at the point (2t, (2)/(t_(1))) meets the curve again at (2t_(2), (2)/(t_(2))) , then

If the normal to the rectangular hyperbola xy=c^(2) at the point t' meets the curve again at t_(1) then t^(3)t_(1), has the value equal to

Statement :1 If a parabola y ^(2) = 4ax intersects a circle in three co-normal points then the circle also passes through the vertr of the parabola. Because Statement : 2 If the parabola intersects circle in four points t _(1), t_(2), t_(3) and t_(4) then t _(1) + t_(2) + t_(3) +t_(4) =0 and for co-normal points t _(1), t_(2) , t_(3) we have t_(1)+t_(2) +t_(3)=0.

The normal to the rectangular hyperbola xy=4 at the point t_(1), meets the curve again at the point t_(2) Then the value of t_(1)^(2)t_(2) is

If a circle cuts a rectangular hyperbola xy=1 in four points P,Q,R,S and the parameters of these four points be t_(1),t_(2),t_(3) and t_(4) respectively and -20t_(1)t_(2)t_(3)t_(4)=k , then value of k equals

The point of intersection of tangents at 't'_(1) " and " 't'_(2) to the hyperbola xy = c^(2) is

[" 18.If the normal at " t_(1) " on the hyperbola " xy=c^(2) " meets the hyperbola at t_(2) then

Find t_5 and t_6 of the arithmetic progression 0, (1)/(4), (1)/(2), (3)/(4),…. .

ARIHANT MATHS-HYPERBOLA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Statement-I If a circle S=0 intersect hyperbola xy=4 at four points, t...

    Text Solution

    |

  2. The locus a point P(alpha,beta) moving under the condition that the li...

    Text Solution

    |

  3. Let a hyperbola passes through the focus of the ellipse (x^(2))/(25)+(...

    Text Solution

    |

  4. A hyperbola, having the transverse axis of length 2sin theta, is conf...

    Text Solution

    |

  5. Two braches of a hyperbola

    Text Solution

    |

  6. For the hyperbola (x^2)/(cos^2alpha)-(y^2)/(sin^2alpha)=1 , which of ...

    Text Solution

    |

  7. Consider a branch of the hypebola x^2-2y^2-2sqrt2x-4sqrt2y-6=0 with ve...

    Text Solution

    |

  8. An ellipse intersects the hyperbola 2x^(2)-2y^(2)=1 orthogonally. The ...

    Text Solution

    |

  9. The circle x^(2)+y^(2)-8x=0 and hyperbola (x^(2))/(9)-(y^(2))/(4)=1 in...

    Text Solution

    |

  10. The circle x^2+y^2-8x=0 and hyperbola x^2/9-y^2/4=1 intersect at the...

    Text Solution

    |

  11. The line 2x + y = 1 is tangent to the hyperbola x^2/a^2-y^2/b^2=1. I...

    Text Solution

    |

  12. Let P(6,3) be a point on the hyperbola parabola x^2/a^2-y^2/b^2=1If t...

    Text Solution

    |

  13. let the eccentricity of the hyperbola x^2/a^2-y^2/b^2=1 be reciprocal ...

    Text Solution

    |

  14. Tangents are drawn to the hyperbola x^2/9-y^2/4=1 parallet to the srai...

    Text Solution

    |

  15. Consider the hyperbola H:x^2-y^2=1 and a circle S with centre N(x2,0) ...

    Text Solution

    |

  16. The eccentricity of the hyperbola whose latuscrectum is 8 and conjugat...

    Text Solution

    |

  17. A hyperbola passes through the point P(sqrt(2),sqrt(3)) and has foci a...

    Text Solution

    |

  18. If 2x-y+1=0 is a tangent to the hyperbola (x^2)/(a^2)-(y^2)/(16)=1 the...

    Text Solution

    |