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Q.

There is a point (p,q) on the graph of fx=x2 and a point r,s  on the graph of gx=8x , where   p>0 and r>0. If the line through p,q  and  r,s is also tangent to both the curve at these points, respectively, then the value of pr is ____

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answer is 3.

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Detailed Solution

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y=x2  and  y=8x
q=p2  and  s=8r
Equating dydx  at A and B
We get  2p=8r2  or  pr2=4 
Now,  mAB=qspr     or     2p=p2+8rpr   or  p2=2pr+8r

or  p2=16r     or   16r4=16r=    or    r=1r0      or   p=4
    r=1,p=4   Hence,   pr=3

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