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Question

3. centreand radius2' 412

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Solution

The given center of circle is ( 1 2 , 1 4 ) and the radius is 1 12 .

The formula for the equation of circle is given by,

( xh ) 2 + ( yk ) 2 = r 2 (1)

Where h and k denotes the center of the circle and r denotes the radius of the circle.

From the question, h= 1 2 ,k= 1 4 and r= 1 12

Substitute the values of h, k and r in equation (1), to find the equation of circle.

( x 1 2 ) 2 + ( y 1 4 ) 2 = 1 144 x 2 + 1 4 x+ y 2 + 1 16 1 2 y= 1 144 144 x 2 + 144 4 144x+144 y 2 + 144 16 144 2 y=1 144 x 2 +36144x+144 y 2 +972y1=0 144 x 2 144x+144 y 2 72y+44=0 36 x 2 36x+36 y 2 18y+11=0

Thus the equation of the circle with center ( 1 2 , 1 4 ) and radius 1 12 is. 36 x 2 36x+36 y 2 18y+11=0 .


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