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The straight kine y=mx+c(m>0) touches the parabola y^2=8(x+2) then the minimum value taken by c is

The straight kine y=mx+c(m>0) touches the parabola y^2=8(x+2) then the minimum value taken by c is

Grade:11

1 Answers

Abhishek Singh
105 Points
9 years ago
given y2=8(x+2) , we put X=x+2 so eqn is transformed to 
y2 = 8X,
Then eqn of line   y=mx+c is transformed to  y=m(X-2)+c   -------------->  y=mX-2m+c
For a given line to be tangent to a parabola,
 (constant term)(slope)=(a of parabola)                   ( we get a by comparing with y2=4ax std.parabola)
(c-2m)(m)=2
c= 2/m + 2m
using am -gm inequality min. value of c is 4.                
 
 

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