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Question
Find the equation of the circle with centre on the X-axis and passing through the origin having radius 4.
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Solution
Let the co-ordinates of the centre of the required circle be C(h, 0).
Since the circle passes through the origin i.e., O(0,0),
OC = radius
∴ `sqrt(("h" - 0)^2 + (0 - 0)^2` = 4
∴ h2 = 16
∴ h = ± 4
∴ the co-ordinates of the centre are (4, 0) or (– 4, 0).
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 = ± 4, k = 0, r = 4
∴ The required equation of the circle is
(x – 4)2 + (y – 0)2 = 42 or (x + 4)2 + (y – 0)2 = 42
∴ x2 – 8x + 16 + y2 = 16 or x2 + 8x + 16 + y2 = 16
∴ x2 + y2 – 8x = 0 or x2 + y2 + 8x = 0
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