If a tangent to the curve $y = 6 x - x^{2}$ is parallel to the line $4 x - 2 y - 1 = 0$ , then the point of tangency on the curve is:

(2, 8)

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(8, 2)

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(6, 1)

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(4, 2)

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Solution

The correct option is A (2, 8)
$y = 6 x - x^{2}$
$\Rightarrow y^{'} = 6 - 2 x a s t a n g e n t i s p a r a l l e l t o l i n e 4 x - 2 y - 1 = 0$ slope $= 2$
$\Rightarrow 6 - 2 x = 2$
$\Rightarrow x = 2$
So $y = 6 \cdot 2 - 2^{2} = 8$
Hence the point of tangency is $(2, 8)$

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