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The focal chord to y^2=16 x is tangent t...

The focal chord to `y^2=16 x` is tangent to `(x-6)^2+y^2=2.` Then the possible value of the slope of this chord is (a)`{-1,1}` (b) `{-2,2}` (c)`{-2,1/2}` (d) `{2,-1/2}`

A

{-1,1}

B

{-2,2}

C

(-2,1/2}

D

{2,-1/2}

Text Solution

Verified by Experts

The correct Answer is:
A
Here, the focal chord of `y^(2) = 16 x` is tangent to circle `(x - 6)^(2) + y^(2) = 2`
`implies` Focus of parabola as (a,0) i., (4.0) ,
Now, tangents are drawn from (4,0) to `(x - 6)^(2) + y^(2) = 2`
since, PA is tangent to circle
`:. tan theta` = slope of tangent `= (AC)/(AP) = (sqrt(2))/(sqrt(2)) = 1`, or `(BC)/(BP) = -1`
`:.` Slope of focal chord as tangent to circle = `+-` 1
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