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Question

The equation of the normal to the circle x2+y22x=0 parallel to the line x + 2y = 3 is .

A
x + 2y - 1 = 0
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B
x - 2y + 1 = 0
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C
x + 2y + 1 = 0
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D
x - 2y - 1 = 0
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Solution

The correct option is A x + 2y - 1 = 0
the center of the given circle is (1,0).
Any line parallel to x + 2y = 3 is given by x + 2y + k = 0
And we know that normal passes through the center of the circle
1 + 2(0) + k = 0
k = -1
Hence, the equation of the normal will be : x + 2y - 1 = 0

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