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

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Wed Oct 07, 2020 10:59 am

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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

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Source: Beat The GMAT — Problem Solving | Wed Oct 07, 2020 10:59 am

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Re: A circle in the coordinate plane passes through points $(-3, -2)$ and $(1, 4).$ What is the smallest possible ar

by Scott@TargetTestPrep » Sun Oct 11, 2020 5:32 am

Gmat_mission wrote: ↑
Wed Oct 07, 2020 10:59 am
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

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