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 `{-1,1}` (b) `{-2,2}` `{-2,1/2}` (d) `{2,-1/2}`

Options

A. (-1, 1)
B. (-2, 2)
C. (-2, 1/2)
D. (2, -1/2)

Answer

A

Explanation

The coordinates of the focus of the parabola `y^(2)=16x` are (4, 0).
The equation of tangents of slope m to the circlen
`(x-6)^(2)+(y-0)^(2)=(sqrt2)^(2)" are "y=m(x-6)+-sqrt2sqrt(1+m^(2))`
If these tangents pass through the focus i.e. (4, 0) then
`0=-2m+-sqrt2sqrt(1+m^(2))`
`rArr" "4m^(2)=2(1+m)^(2)rArr2m^(2)=2rArrm=+-1`