Home
Class 12
MATHS
The values of m for which the lines y ...

The values of m for which the lines y = mx + ` 2 sqrt5` touches the hyperbola ` 16 x^(2) - 9y^(2) = 144` are the roots of ` x^(2) - (a+b) x-4 = 0 ` then the value of (a+b) is

A

2

B

4

C

zero

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
The equation of the hyperbola is
`(x^(2))/(9)-(y^(2))/(16)=1`
The equation of the tangent is
`y=mx+sqrt(9x^(2)-16)`
`"or sqrt(9m^(2)-16)=2sqrt5`
`"or "m= pm2`
or a + b = sum of roots = 0
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    CENGAGE|Exercise Exercise (Multiple)|18 Videos

  • HYPERBOLA

    CENGAGE|Exercise Exercise (Comprehension)|21 Videos

  • HYPERBOLA

    CENGAGE|Exercise Exercise 7.6|4 Videos

  • HIGHT AND DISTANCE

    CENGAGE|Exercise JEE Previous Year|3 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Question Bank|21 Videos

Similar Questions

Explore conceptually related problems

The vertices of the hyperbola 9x^2 - 16y^2 = 144

Find the value of c if y = x + c is a tangent to the hyperbola 9x^(2) -16y^(2) = 144

The value of m, for wnich the line y=mx + 25sqrt3/3 is a normal to the conic x^2 /16 - y^2 / 9 =1 , IS

Prove that the line 5x+12y=9 touches the hyperbola x^(2)-9y^(2)=9 and find the point of contact.

If the line 2x+sqrt6y=2 touches the hyperbola x^2-2y^2=4 , then the point of contact is

Find the vertices, foci for the hyperbola 9x^(2)-16y^(2)=144.

Find the vertices, foci for the hyperbola 9x^(2)-16y^(2)=144 .

Show that the line x + y + 1=0 touches the hyperbola x^(2)/16 -y^(2)/15 = 1 and find the co-ordinates of the point of contact.

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

    Text Solution

    |

  2. about to only mathematics

    Text Solution

    |

  3. The values of m for which the lines y = mx + 2 sqrt5 touches the hy...

    Text Solution

    |

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

    Text Solution

    |

  5. The sides A Ca n dA B of a A B C touch the conjugate hyperbola of the...

    Text Solution

    |

  6. The number of possible tangents which can be drawn to the curve 4x^2-9...

    Text Solution

    |

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

    Text Solution

    |

  8. Locus of the feet of the perpendiculars drawn from either foci on a va...

    Text Solution

    |

  9. P is a point on the hyperbola (x^(2))/(y^(2))-(y^(2))/(b^(2))=1, and N...

    Text Solution

    |

  10. Find the point on the curve 3x^2-4y^2=72 which is nearest to the line ...

    Text Solution

    |

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

    Text Solution

    |

  12. The locus of a point, from where the tangents to the rectangular hy...

    Text Solution

    |

  13. If tangents P Qa n dP R are drawn from a variable point P to thehyperb...

    Text Solution

    |

  14. The number of points on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=3 from w...

    Text Solution

    |

  15. If a ray of light incident along the line 3x+(5-4sqrt(2))y=15 gets ref...

    Text Solution

    |

  16. The chord of contact of a point P w.r.t a hyperbola and its auxiliary ...

    Text Solution

    |

  17. The ellipse 4x^2+9y^2=36 and the hyperbola a^2x^2-y^2=4 intersect at r...

    Text Solution

    |

  18. The locus of the point which is such that the chord of contact of t...

    Text Solution

    |

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

    Text Solution

    |

  20. If the tangent at point P(h, k) on the hyperbola (x^(2))/(a^(2))-(y^(2...

    Text Solution

    |