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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????

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????

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2 Answers

vikas askiitian expert
509 Points
10 years ago

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

DanishABDV
19 Points
4 years ago
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

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