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Question
Find the equation of the circle with centre at (a, b) touching the Y-axis
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Solution
Since the circle is touching the Y-axis,
radius of the circle is X-co-ordinate of the centre.
∴ r = a
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 = a, k = b
∴ The required equation of the circle is
(x – a)2 + (y – b)2 = a2
∴ x2 – 2ax + a2 + y2 – 2by + b2 = a2
∴ x2 + y2 – 2ax – 2by + b2 = 0
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