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Q.
The number of tangents that can be drawn from $\left(2 , 0\right)$ to the curve $y=x^{6}$ is/are
NTA AbhyasNTA Abhyas 2020Application of Derivatives
Solution:
Let $A$ be $\left(\alpha , \left(\alpha \right)^{6}\right)$ & $B$ be $\left(2,0\right)$
So, slope of $AB=6\alpha ^{5}=\frac{\alpha ^{6}}{\alpha - 2}$
$\Rightarrow \alpha =0$ or $6\alpha -12=\alpha $
$\Rightarrow \alpha =0$ or $\alpha =\frac{12}{5}$
$\Rightarrow 2$ tangents are possible
