the focal chord of y raise to the power 2=16x is tangent to (x-6) whole square+ y raise to the power 2=2 , then the possible values of the slope of this chord, are????

y² = 16x

comparing this with y² = 4ax we get

focus of this parabola is at (a,0) = (4,0)

now focal chord : y = m(x-4)                  ..................1

m is slope of this chord....

this chord is tangent of (x-6)² + y² = 2

this is equation of circle ...

for circle x²+y² = a²  if line is tangent then its equation is given by

y = mx +(-)a(1+m²)  

for (x-6)² + y² = 2 tangent will be

y = m(x-6) +(-)a(1+m²)^1/2

y = mx - 6m +(-)(2+2m²)^1/2                 ..................2

eq 2 & eq 1 are same line so

-4m = -6m +(-)(2+2m²)^1/2                           (equating intercepts)

 2m = (2+2m²)^1/2

m² = 1

m = +(-) 1

therefore possible values for m are +1 & -1

approve if u like my ans

Approved

Centre of circle is (6,0) and radius=√2Eqn of focal chord passing through focus(4,0) of parabola is y-0=m(x-4)mx-4m-y=0Perpendicular distance from centre(6,0) to focal chord is|6m-4m-0|÷√1+m^2=√2Squaring both sides4m^2=2m^2+2m^2=1m=+1 and -1