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Question: The equation of the image of the circle (x –3)<sup>2</sup> + (y – 2)<sup>2</sup> = 1 by the mirror x...

The equation of the image of the circle (x –3)2 + (y – 2)2 = 1 by the mirror x + y = 19 is

A

(x –14)2 + (y –13)2 = 1

B

(x –15)2 + (y –14)2 = 1

C

(x – 16)2 + (y –15)2 = 1

D

(x –17)2 + (y –16)2 = 1

Answer

(x –17)2 + (y –16)2 = 1

Explanation

Solution

C¢ is the image point of C about line x + y = 19

x−31\frac{x - 3}{1}= y−21\frac{y - 2}{1}= –2(1+2−19)2\frac{(1 + 2 - 19)}{2}

x−31\frac{x - 3}{1}=y−21\frac{y - 2}{1}= 14

x = 17, y = 16

equation of image circle (x – 17)2 + (y – 16)2 = 1