The equation of the image of the circle x 2 + y 2 - 6x - 4y + 12 = 0 by the line mirror x + y - 1 = 0 Options: A . &nbspx2+y2 + 2x + 4y + 4 = 0 B . &nbspx2+y2 - 2x + 4y + 4 = 0 C . &nbspx2+y2 + 2x + 4y - 4 = 0 D . &nbspx2+y2 + 2x - 4y - 4 = 0

The equation of the image of the circle x2+y2 - 6x

Question

The equation of the image of the circle

x^{2} + y^{2}

- 6x - 4y + 12 = 0 by the line mirror x + y - 1 = 0

Options:

A . x2+y2 + 2x + 4y + 4 = 0

B . x2+y2 - 2x + 4y + 4 = 0

C . x2+y2 + 2x + 4y - 4 = 0

D . x2+y2 + 2x - 4y - 4 = 0

Answer: Option A
:
A
For the circle

x^{2} + y^{2}

- 6x - 4y + 12 = 0.
This circle hascentre 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

x^{2} + y^{2}

- 6x - 4y + 12 = 0 w.r.t x + y - 1 = 0 is,

x^{2} + y^{2}

+ 2x + 4y + 4 = 0

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