Home
Class 11
MATHS
If the line y=3x+lambda touches the hype...

If the line `y=3x+lambda` touches the hyperbola `9x^2-5y^2=45`, then the value of `lambda` is

A

`+-3sqrt(6)`

B

`+-6`

C

`+-3`

D

`+-4`

Text Solution

Verified by Experts

The correct Answer is:
B
The equation of the hyperbola is
`9x^(2)-5y^(2)=45implies(x^(2))/(5)-(y^(2))/(9)=1`……`(ii)`
This of the form `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`, where `a^(2)=5` and` b^(2)=9`.
The line `y=3x+lambda` will touch the given hyperbola, if
`lambda^(2)=5(3)^(2)-9` [Using : `c^(2)=a^(2)m^(2)-b^(2)`]
`implieslambda^(2)=36implieslambda=+-6`
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|54 Videos

  • HYPERBOLA

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|4 Videos

  • FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|29 Videos

  • INEQUALITIES

    OBJECTIVE RD SHARMA ENGLISH|Exercise EXERCISE SECTION-II (Assertion-Reason )|1 Videos

Similar Questions

Explore conceptually related problems

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

The line y=x+2 touches the hyperbola 5x^2-9y^2=45 at the point

If the line y=2x+lambda be a tangent to the hyperbola 36x^(2)-25y^(2)=3600 , then lambda is equal to

The line 4y - 3x + lambda =0 touches the circle x^2 + y^2 - 4x - 8y - 5 = 0 then lambda=

If a circle passes through the points of intersection of the lines 2x-y +1=0 and x+lambda y -3=0 with the axes of reference then the value of lambda is :

Two lines (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (x-4)/(5)=(y-1)/(2)=(z)/(1) intersect at a point P. If the distance of P from the plane 2x-3y+6z=7 is lambda units, then the value of 49lambda is equal to

If the line 3x-4y-lambda=0 touches the circle x^2 + y^2-4x-8y- 5=0 at (a, b) then which of the following is not the possible value of lambda+a + b ?

If the line 3x-4y-lambda=0 touches the circle x^2 + y^2-4x-8y- 5=0 at (a, b) then which of the following is not the possible value of lambda+a + b ?

If the curves C_1 : y= (In x)/x and C_2 : y=lambdax^2 (where lambda is constant) touches each other, then the value of lambda is

If a circle passes through the point of intersection of the lines x+ y +1=0 and x+ lambda y-3=0 with the coordinate axis, then find the value of lambda .

OBJECTIVE RD SHARMA ENGLISH-HYPERBOLA-Chapter Test
  1. If the line y=3x+lambda touches the hyperbola 9x^2-5y^2=45, then the v...

    Text Solution

    |

  2. Find the value of m for which y=m x+6 is tangent to the hyperbola (x^2...

    Text Solution

    |

  3. The equation of the tangent to the hyperbola 4y^(2)=x^(2)-1 at the poi...

    Text Solution

    |

  4. The number of normals to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))...

    Text Solution

    |

  5. If e and e1 are the eccentricities of the hyperbola xy=c^(2) and x^(2)...

    Text Solution

    |

  6. A rectangular hyperbola with centre C, is intersect by a circle of rad...

    Text Solution

    |

  7. The equation of the pair of asymptotes of the hyperbola xy-4x+3y=0, is

    Text Solution

    |

  8. If the latus rectum of the hyperbola (x^(2))/(16)-(y^(2))/(b^(2))=1 is...

    Text Solution

    |

  9. Chords of the hyperbola x^(2)-y^(2)=a^(2) touch the parabola y^(2)=4ax...

    Text Solution

    |

  10. Tangents drawn from the point (c, d) to the hyperbola (x^(2))/(a^(2))-...

    Text Solution

    |

  11. If the tangent at (h, k) on b^2x^2-a^2y^2=a^2b^2 cuts the auxiliary ci...

    Text Solution

    |

  12. If the chords of contact of tangents drawn from P to the hyperbola x^(...

    Text Solution

    |

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

    Text Solution

    |

  14. The mid-point of the chord intercepted by the hyperbola 9x^(2)-16y^(2)...

    Text Solution

    |

  15. Locus of P such that the chord of contact of P with respect to y^2=4ax...

    Text Solution

    |

  16. C is the center of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 The tangen...

    Text Solution

    |

  17. If lx+my+n=0 is a tangent to the rectangular hyperbola xy=c^(2), then

    Text Solution

    |

  18. A tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 cuts the ellipse ...

    Text Solution

    |

  19. The product of lengths of perpendicular from any point on the hyperbol...

    Text Solution

    |

  20. The angle between the asymptotes of the hyperbola 3x^(2)-y^(2)=3, is

    Text Solution

    |

  21. Find the area of the triangle formed by any tangent to the hyperbola (...

    Text Solution

    |