A) \[y=0\]
B) \[x=0\]
C) \[x+y=0\]
D) None of these
Correct Answer: A
Solution :
Let the point of contact be \[(h,k)\], where \[k={{h}^{4}}\]. Tangent is \[y-k=4{{h}^{3}}(x-h)\], \[\left[ \because \,\frac{dy}{dx}=4{{x}^{3}} \right]\] It passes through (2, 0), \ \[-k=4{{h}^{3}}(2-h)\]\[\] Þ \[h=0\]or 8/3 , \ \[k=0\] or (8/3)4 \ Points of contact are (0, 0) and \[\left( \frac{8}{3},\,{{\left( \frac{8}{3} \right)}^{4}} \right)\] \ Equation of tangents are \[y=0\] and\[y-{{\left( \frac{8}{3} \right)}^{4}}=4{{\left( \frac{8}{3} \right)}^{3}}\left( x-\frac{8}{3} \right)\].
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