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Question
Find the equation of a circle with radius 4 units and touching both the co-ordinate axes having centre in third quadrant.
Solution
Radius of the circle = 4 units
Since the circle touches both the co-ordinate axes and its centre is in third quadrant,
the centre of the circle is C (– 4, – 4).
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 = – 4, r = 4
∴ the required equation of the circle is
[x – (– 4)]2 + [y – (– 4)]2 = 42
∴ (x + 4)2 + (y + 4)2 = 16
∴ x2 + 8x + 16 + y2 + 8y + 16 – 16 = 0
∴ x2 + y2 + 8x + 8y + 16 = 0.
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