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A circle is given by the equation x² + y² + 16x - 24y + 183 = 0. If this circle is reflected in the line 4x + 7y + 13 = 0, what is the equation of the resulting image circle?
- x² + y² + 32x - 4y + 235 = 0
- x² + y² + 32x + 235 = 0
- x² + y² + 32x - 4y - 235 = 0
- x² + y² + 32x + 4y + 235 = 0
Correct answer: x² + y² + 32x + 4y + 235 = 0
Solution
The circle has centre (-8,12), r=5. Reflecting (-8,12) in 4x+7y+13=0 gives the image centre (-16,-2), radius still 5. The image circle is (x+16)^2+(y+2)^2=25, i.e. x^2+y^2+32x+4y+235=0.
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