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

Let `P(a sec theta,b tan theta)` and `Q(a sec varphi, b tan varphi)` where `theta+varphi=(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=`

A

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

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|172 Videos

  • INDEFINITE INTEGRAL

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|404 Videos

Similar Questions

Explore conceptually related problems

x = a sec theta, y = b tan theta .

Let P(6,3) be a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 . If the normal at the point P intersect the x -axis at (9,0) then the eccentricity of the hyperbola is

Locus of the point of intersection of the tangents at the points with eccentric angles phi and (pi)/(2) - phi on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is

If theta is the angle between the asymptotes of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 with eccentricity is e then sec ((theta)/(2))=

The distance of the point theta^(prime) on the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 from a focus is

If tan theta=(1)/(2) and tan varphi=(1)/(3) then the value of theta+varphi is

Solve sqrt(2) sec theta+tan theta=1 .

If x=a sin theta and y=b tan theta , then find the value of (a^(2))/(x^(2))-(b^(2))/(y^(2))

Prove that (sec theta + tan theta)^(2) = (cosec theta +1)/(cosec theta -1) .

HIMALAYA PUBLICATION-HYPERBOLA-QUESTION BANK
  1. The equation of a tangent parallel to y=x drawn to (x^(2))/(3)-(y^(2))...

    Text Solution

    |

  2. The eccentricity of the hyperbola 9 x^(2)-16 y^(2)-18 x-64 y-199=0 i...

    Text Solution

    |

  3. Let P(a sec theta,b tan theta) and Q(a sec varphi, b tan varphi) where...

    Text Solution

    |

  4. The equation (x^(2))/(1-r)+(y^(2))/(r-3)+1=0 represents an ellipse if ...

    Text Solution

    |

  5. If the line y=3 x+lambda touches the hyperbola 9 x^(2)-5 y^(2)=45, the...

    Text Solution

    |

  6. The equation to the normal to the hyperbola (x^(2))/(16)-(y^(2))/(9)=1...

    Text Solution

    |

  7. If the circle x^(2)+y^(2)=a^(2) intersects the hyperbola xy=c^(2) in f...

    Text Solution

    |

  8. The distance of the focua of x^(2)-y^(2)=4 from the directrix which is...

    Text Solution

    |

  9. The equation of a hyperbola whose asymtotes are 3xpm5y=0 and vertices ...

    Text Solution

    |

  10. If e1 and e2 are the eccentricities of a hyperbola and its conjugate t...

    Text Solution

    |

  11. The distance between the directrices of the hyperbola x=8sectheta,y=8t...

    Text Solution

    |

  12. If x = 9 is the chord of contact of the hyperbola x^2-y^2=9 , then the...

    Text Solution

    |

  13. If e(1) is the eccentricity of the ellipse (x^(2))/(16)+(y^(2))/(25)=1...

    Text Solution

    |

  14. A hyperbola having the transversal axis of length 2sintheta is confoca...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. The equation of the common tangents to the circle x^(2)+y^(2)=2 a^(2) ...

    Text Solution

    |

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

    Text Solution

    |

  19. The line 3 x+4 y+5=0 is a tangent to the hyperbola x^(2)-4 y^(2)=5 at

    Text Solution

    |

  20. Let P(6,3) be a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))...

    Text Solution

    |