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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
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