Q4 of 63 Page 202

Find the equation of the circle which touches x-axis and whose centre is (1, 2).

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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