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Question
Find the equation of the circle with centre at (–2, 3) touching the X-axis.
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Solution
The centre of the circle is (–2, 3).
Since it touches the X-axis, its radius = |3| = 3.
The equation of a circle with centre at (h, k) and radius r is given by
(x – h)2 + (y – k)2 = r2
Here, h = −2, k = 3
∴ The equation of the circle is
(x + 2)2 + (y – 3)2 = (3)2
∴ x2 + 4x + 4 + y2 – 6y + 9 = 9
∴ x2 +y2 + 4x − 6y + 4 = 0
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