Home
Class 12
MATHS
Let P(a sec theta , b tan theta ) and Q...

Let ` P(a sec theta , b tan theta ) and Q(a sec phi , b tan phi)` where ` theta + phi = (pi)/(2) ` be two point on the hyperbola ` (x^(2))/(a^(2)) - (y^(2))/(b^(2)) =1 ` .If ( h, k) be the point of intersection of the normals at P and Q , then the value of k is -

A

`(a^(2) +b^(2))/(a) `

B

`-(a^(2) +b^(2))/(a) `

C

`(a^(2) +b^(2))/(b) `

D

`-(a^(2) +b^(2))/(b) `

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • MCQ ZONE 3

    CHHAYA PUBLICATION|Exercise Question Paper 2|30 Videos
  • MCQ ZONE 3

    CHHAYA PUBLICATION|Exercise Question Paper 3|30 Videos
  • MCQ ZONE

    CHHAYA PUBLICATION|Exercise Question Paper 7|80 Videos
  • MCQ's

    CHHAYA PUBLICATION|Exercise QUESTION PAPER 9|66 Videos

Similar Questions

Explore conceptually related problems

Let P(a sectheta, btantheta) and Q(asecphi , btanphi) (where theta+phi=pi/2 ) be two points on the hyperbola x^2/a^2-y^2/b^2=1 If (h, k) is the point of intersection of the normals at P and Q then k is equal to (A) (a^2+b^2)/a (B) -((a^2+b^2)/a) (C) (a^2+b^2)/b (D) -((a^2+b^2)/b)

The slop of the normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point ( a sec theta , b tan theta) is -

If x=a sin theta and y=b tan theta , then prove that (a^(2))/(x^(2))-(b^(2))/(y^(2))=1 .

Find the equation of tangent at the specified point on the following curve : (x^(2))/(a^(2))-(y^(2))/(b^(2))=1" at"( a sec theta, b tan theta)

If x=a sec theta cosphi, y = b sec theta sin phi and z=c tan theta , then prove that (x^(2))/(a^(2))+(y^(2))/(b^(2))-(z^(2))/(c^(2))=1.

If (1+ tan theta) (1+ tan phi)=2, then the value of (theta+ phi) is

P (a sec phi , a tan phi) is a variable point on the hyperbola x^(2) - y^(2) = a^(2) , and A(2a,0) is a fixed point. Prove that the locus of the middle point of AP is a rectangular hyperbola.

If " "a cos phi = b cos theta," show that " a tan theta + b tan phi = (a+b) tan ((theta + phi)/2)

If 3 tan theta tan phi=1 , then prove that 2 cos (theta+phi)=cos (theta-phi) .

Find the equation of the normal at the specified point to each of the following curves (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 "at" ( a sec theta, b tan theta)

CHHAYA PUBLICATION-MCQ ZONE 3 -Question Paper 8
  1. Let P(a sec theta , b tan theta ) and Q(a sec phi , b tan phi) where ...

    Text Solution

    |

  2. If the line y=2x+k is a tangent to the curve x^(2)=4y, then the value ...

    Text Solution

    |

  3. The are (in square unit ) bounded by the parabola x^(2)=16y, y-axis an...

    Text Solution

    |

  4. The tangent drawn at the point (0, 1) on the curve y=e^(2x) meets the ...

    Text Solution

    |

  5. The area (in square unit) bounded by the curve f(x)=4-|x| and the x-a...

    Text Solution

    |

  6. If the area bounded by the parabola y=x-x^(2) and the line y=mx is (9)...

    Text Solution

    |

  7. The point of intersection of the tangents to the parabola y^(2)=4ax at...

    Text Solution

    |

  8. The locus of the point of intersection of two perpendicular tangents t...

    Text Solution

    |

  9. If the area bounded by the parabola y=2-x^(2) and the line x+y=0 is A...

    Text Solution

    |

  10. The angle between the tangents drawn from the point (1, 4) to the pa...

    Text Solution

    |

  11. The area (in square unit) of the region bounded by the curve y=|x-2|...

    Text Solution

    |

  12. If the line 2x+sqrt(6)y=2 is a tangent to the hyperbola x^(2)-2y^(2)=...

    Text Solution

    |

  13. The equation of the normal to the curve x^(3)+y^(3)=8xy at the point w...

    Text Solution

    |

  14. The curve x=1-3t^(2), y=t-3t^(3) is symmetrical with respect to -

    Text Solution

    |

  15. The equation of the curve in which the portion of the tangent between...

    Text Solution

    |

  16. The equation of the normal to the parabola y^(2)=5x. Which makes an a...

    Text Solution

    |

  17. The maximum value of Z=3x+4y subject to the constraints x+y le 40, x...

    Text Solution

    |

  18. The minimum value of (1)/(2)(7-cos2x) is -

    Text Solution

    |

  19. If g(x)=min(x, x^(2)) where x is a real number then -

    Text Solution

    |

  20. The value of a so that the sum of the squares of the roots of the equ...

    Text Solution

    |

  21. Twenty metres are available to fence a land in the form of a circular...

    Text Solution

    |