A graphic designer is drawing a pattern of four concentric circles on the coordinate plane. the center of the circles is located at (-2, 1). The smallest circle has a radius of 1 unit. If the radius of each of the circles is one unit greater than the largest circle within it, what would be the equation of the fourth circle?
Radius of first circle is 1 unit, so radius of second circle will be 2 units, third will be 3 units and fourth will be 4 units.
For equation of circle use the formula,
( x - a ) ^ 2 + ( y - b ) ^ 2 = r ^ 2
where ( a , b ) is the centre of the circle and r is radius.
Since circles are concentric centre will be the same. So, the equation is
( x - (- 2)) ^ 2 + ( y - 1 ) ^ 2 = 4 ^ 2
( x + 2) ^ 2 + ( y - 1 ) ^ 2 = 16
x ^ 2 + y ^ 2 + 4x - 2y - 11 = 0