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Determine the equation of the normal to the circle x² + y² = 2x that is parallel to the line x + 2y = 3.

1. x + 2y = 0
2. 2x - y = 0
3. x - 2y = 0
4. 2x + y = 0

Correct answer: x + 2y = 0

Solution

The circle x²+y²=2x has centre (1,0); a normal parallel to x+2y=3 is x+2y = k passing through (1,0), giving k = 1... check options: line through (1,0) with slope -1/2 is x + 2y = 1, but the matching option family is x+2y=0; using centre (1,0) actually gives x+2y=1, so re-evaluate.

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