A circle in the coordinate plane passes through points \((-3, -2)\) and \((1, 4).\) What is the smallest possible area

[Gmat_mission]

A circle in the coordinate plane passes through points \((-3, -2)\) and \((1, 4).\) What is the smallest possible area of that circle?

A. \(13\pi\)
B. \(26\pi\)
C. \(262\sqrt{\pi}\)
D. \(52\pi\)
E. \(64\pi\)

Answer: A

Source: Veritas Prep

[Scott@TargetTestPrep]

A circle in the coordinate plane passes through points \((-3, -2)\) and \((1, 4).\) What is the smallest possible area of that circle?

A. \(13\pi\)
B. \(26\pi\)
C. \(262\sqrt{\pi}\)
D. \(52\pi\)
E. \(64\pi\)

Answer: A

Solution:

The circle with the smallest possible area that passes through the points (-3, -2) and (-1, 4) is a circle with a diameter whose endpoints are these two points. We use the distance formula to determine the length of d:

√[(-3 - 1)^2 + (-2 - 4)^2] = √[16 + 36] = √52 = 2√13

Thus, the radius has a length of r = √13, and the area of the circle is A = π x (√13)^2 = 13π.

Answer: A