Find the equation of the normal to the circle $x^{2} + y^{2} = 2 x$ which is parallel to the line $x + 2 y = 3$

x + 2 y - 1 = 0

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x + 2 y + 1 = 0

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x + 2 y - 5 = 0

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x + 2 y + 5 = 0

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Solution

The correct option is A $x + 2 y - 1 = 0$
The centre of the circle is $(1, 0)$ .The required line passes through this centre and parallel to the line with slope $- \frac{1}{2}$ .
Hence the equation becomes $x + 2 y = 1$ .

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