Question

1.centre (0,2) and radius 2

Answer 1

The given center of circle is ( 0,2 ) and the radius is 2.

The formula for the equation of circle is given by,

( x−h ) 2 + ( y−k ) 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=0,k=2 and r=2

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

( x−0 ) 2 + ( y−2 ) 2 =4

Square both the sides of the above equation.

( x−0 ) 2 + (y−2) 2 =4 x 2 + y 2 +4−4y=4 x 2 + y 2 −4y=4−4 x 2 + y 2 −4y=0

Thus, the equation of the circle with center ( 0,2 ) and radius 2 is x 2 + y 2 −4y=0 .