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  4. The number of tangents that can be drawn from (2 , 0) to the curve y=x6 is/are

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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 2022

Solution:

Solution
Let $A$ be $\left(\alpha, \alpha^{6}\right) \& B$ be $(2,0)$
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