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)

graphic-designer

#1

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?

Answer:

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