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The equation of a common tangent to the ...

The equation of a common tangent to the curves `y^(2)=8x` & `xy= -1` is

A

`y= x+2`

B

`y=2x+1`

C

`y=(x)/(2)+4`

D

`y=3x+(2)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
Equation of tangent to the parabola `y^(2)=8x` is
`y=mx +(2)/(m)" "…(i)`
Equation (i) is also a tangent of xy = -1
`:.x(mx+(2)/(m))= -1`
`mx^(2)+(2)/(m)*x+1=0`
Condition of tangency. Discrimination of the equation = 0
`(4)/(m^(2)) -4m =0`
`rArr m^(3)=1`
`m=1`
Common tangent is `y=x+2`
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Knowledge Check

  • The equation of common tangent to the curves y^(2)=16x and xy=-4 is

    A
    `y=x+4`
    B
    `2x-y+8=0`
    C
    x+y=4
    D
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  • The equation of the common tangent to the curve y^(2) = 8x " and " xy = - 1 is

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    `3y = 9x + 2`
    B
    `y = 2x + 1`
    C
    `2y = x + 8 `
    D
    `y = x + 2`

  • The equation of the common tangent to the curves y^2 = 8 x and xy=-1 is

    A
    `3y=9x+2`
    B
    `y = 2x +1`
    C
    `2y = x+8`
    D
    `y=x+2`

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