Home
Class 11
MATHS
If tangents drawn from the point (a, 2) ...

If tangents drawn from the point (a, 2) to the hyperbola `(x^(2))/(16)-(y^(2))/(9)=1` are perpendicular, then the value of `a^(2)` is __________.

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

the eccentricity of the hyperbola (x^(2))/(16)-(y^(2))/(25)=1 is

The number of tangents that can be drawn from the point (6, 2) on the hyperbola (x^(2))/(9)-(y^(2))/(4)=1 is

Find the equation of pair of tangents drawn from point (4, 3) to the hyperbola (x^(2))/(16)-(y^(2))/(9)=1 . Also, find the angle between the tangents.

Tangents drawn from the point (c, d) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 make angles alpha and beta with the x-axis. If tan alpha tan beta=1 , then find the value of c^(2)-d^(2) .

If two distinct tangents can be drawn from the point (alpha, alpha+1) on different branches of the hyperbola (x^(2))/(9)-(y^(2))/(16)=1 , then find the values of alpha .

Find the angle between the asymptotes of the hyperbola (x^2)/(16)-(y^2)/9=1 .

Find the lengths of the tangents drawn from the point. (-4,5) to the circle x^(2)+y^(2)=16

The area of triangle formed by the tangents from the point (3, 2) to the hyperbola x^2-9y^2=9 and the chord of contact w.r.t. the point (3, 2) is_____________

If the chords of contact of tangents from two points (-4,2) and (2,1) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are at right angle, then find then find the eccentricity of the hyperbola.

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. lf the eccentricity of the hyperbola x^2 - y^2 sec^2 alpha=5 is sqrt3...

    Text Solution

    |

  2. If L is the length of the latus rectum of the hyperbola for which x = ...

    Text Solution

    |

  3. If the chord x cos theta alpha+y sin alpha=p of the hyperbola (x^(2))...

    Text Solution

    |

  4. If the vertex of a hyperbola bisects the distance between its center ...

    Text Solution

    |

  5. If the distance between two parallel tangents drawn to the hyperbola (...

    Text Solution

    |

  6. The area of triangle formed by the tangents from the point (3, 2) to t...

    Text Solution

    |

  7. If a variable line has its intercepts on the coordinate axes e and e^(...

    Text Solution

    |

  8. If tangents drawn from the point (a, 2) to the hyperbola (x^(2))/(16)-...

    Text Solution

    |

  9. If the hyperbola x^(2)-y^(2)=4 is rotated by 45^(@) in the anticlockwi...

    Text Solution

    |

  10. The coordinates of a point on the hyperbola (x^2)/(24)-(y^2)/(18)=1 wh...

    Text Solution

    |

  11. If the angle between the asymptotes of hyperbola (x^2)/(a^2)-(y^2)/(b^...

    Text Solution

    |

  12. The sides AC and AB of a DeltaABC touch the conjugate hyperbola of the...

    Text Solution

    |

  13. The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 pa...

    Text Solution

    |

  14. If a x+b y=1 is tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , t...

    Text Solution

    |

  15. The locus of a point whose chord of contact with respect to the circle...

    Text Solution

    |

  16. The locus of the feet of the perpendiculars drawn from either focus on...

    Text Solution

    |

  17. If the line 2x+sqrt6y=2 touches the hyperbola x^2-2y^2=4, then the po...

    Text Solution

    |

  18. Consider the graphs of y=Ax^(2) and y^(2)+3=x^(2)+4y, where A is a pos...

    Text Solution

    |

  19. The eccentricity of the hyperbola |sqrt((x-3)^(2)+(y-2)^(2))-sqrt((x...

    Text Solution

    |

  20. If y = mx+c is tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)...

    Text Solution

    |