Last Updated on May 3, 2023
GMAT OFFICIAL GUIDE PS
Solution:
Because the circle passes through point (5,0) and has center (2,-3), we know that the distance between these points is the radius of the circle.
Since we are given the coordinates for each point, the easiest thing to do is to use the distance formula to determine the circle’s radius. The distance formula is:
Distance= √[(x2 – x1)^2 + (y2 – y1)^2]
We are given two ordered pairs, so we can label the following:
x1 = 2
x2 = 5
y1 = -3
y2 = 0
When we plug these values into the distance formula, we have:
Distance= √[(5 – 2)^2 + (0 – (-3))^2]
Distance= √[(3)^2 + (3)^2] Distance= √[9 + 9]
Distance = √[18]
Distance = √9 x √2
Distance = 3 x √2
Thus, we know that the radius = 3 x √2.
Finally, we can use the radius to determine the area of the circle.
area = πr^2
area = π(3 x √2 )^2
area = π(9 x 2 )
area = 18π
Answer: E
