The equation of a circle is x² + y² - 4x + 6y - 12 = 0
Find the equation of the new circle C1, which is a reflection of the circle C in the y-axis.
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Answer:
x² + y² - 4x + 6y - 12 = 0
x² - 4x + y² + 6y - 12 = 0
(x² - 4x + 4) + (y² + 6y + 3²) -12 -4 -9 = 0 ==> sort of completing the square twice
(x -2)² + (y+3)² = 25
(x -2)² + (y+3)² = 5²
Hence, the circle has radius 5 at centre (2, -3)
Since the new circle is a reflection in the y axis, then the centre of the new circle is(-2, -3). The radius remains at 5 units.
Thus, the equation of the new circle is
(x + 2)² + (y + 3)² = 5²
(x + 2)² + (y + 3)² = 25
x² + 4x + 4 + y² + 6y + 9 - 25 = 0
x² + y² + 4x + 6y - 12 = 0
