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Question

The equation of the image of the circle x2+y2 - 6x - 4y + 12 = 0 by the line mirror x + y - 1 = 0

A
x2+y2 + 2x + 4y + 4 = 0
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B
x2+y2 - 2x + 4y + 4 = 0
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C
x2+y2 + 2x + 4y - 4 = 0
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D
x2+y2 + 2x - 4y - 4 = 0
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Solution

The correct option is A x2+y2 + 2x + 4y + 4 = 0
For the circle x2+y2 - 6x - 4y + 12 = 0.
This circle has centre C(3, 2) and radius (r) = 1
Image of (3, 2) w.r.t the line x + y - 1 = 0 = (-1, -2)
Equation of the circle with centre (-1, -2) and radius 1 is,
(x+1)2+(y+2)2 = 1
Image of x2+y2 - 6x - 4y + 12 = 0 w.r.t x + y - 1 = 0 is,
x2+y2 + 2x + 4y + 4 = 0

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