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The equation of the tangent to the hyper...

The equation of the tangent to the hyperbola `2x^(2)-3y^(2)=6`which is parallel to the line `y=3x+4`, is

A

`y=3x+5`

B

`y=3x-5`

C

`y=3x=5 and y=3x-5`

D

none

Text Solution

Verified by Experts

The correct Answer is:
C
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Equation of the tangents to the hyperbola 2x^(2)-3y^(2)=6 which are parallel to the line y=3x+4 is (A)y=3x+-5(B)y=3x+-6 (C) y=3x+-7 (D) None of these

Statement 1: The equations of tangents to the hyperbola 2x^(2)-3y^(2)=6 which is parallel to the line y=3x+4 are y=3x-5 and y=3x+5. Statement 2: For a given slope, two parallel tangents can be drawn to the hyperbola.

Knowledge Check

  • The equation of a tangent to the hyperbola 3x^(2)-y^(2)=3 , parallel to the line y = 2x +4 is

    A
    `y = 2x +3`
    B
    `y = 2x+1`
    C
    `y = 2x+4`
    D
    `y = 2x+2`

  • The equation of a tangent to the hyperbola 3x^(2)-y^(2)=3 parallel to the line y =2x+4 is

    A
    `y=3x+4`
    B
    `y=2x+1`
    C
    `y=2x-2`
    D
    `y=3x+5`

  • The equation of the tangent to the hyperbola x^2-4y^2=36 , which is perpendicular to the line x-y+4=0 is

    A
    `x-y+-2sqrt3=0`
    B
    `x+y+-3sqrt3=0`
    C
    `x+y+-2sqrt3=0`
    D
    `x-y+-3sqrt3=0`

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