Question:
Find the equation of the circle which touches x-axis and whose centre is (1, 2).
Solution:
Since the circle has a centre (1, 2) and also touches x-axis.
Radius of the circle is, r = 2
The equation of a circle having centre (h, k), having radius as r units, is
(x – h)2 + (y – k)2 = r2
So, the equation of the required circle is:
(x – 1)2 + (y – 2)2 = 22
⇒x2 – 2x + 1 + y2 – 4y + 4 = 4
⇒ x2 + y2 – 2x – 4y + 1 = 0
The equation of the circle is x2 + y2 – 2x – 4y + 1 = 0.
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