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## GMAT - Problem Solving - Coordinate geometry

### In the coordinate plane, a circle has center (2, -3) and passes through the point (5, 0). What is the area of the circle?

In the coordinate plane, a circle has center (2, -3) and passes through the point (5, 0). What is the area of the circle?

Radius of the circle = distance between the center and the point through which the circle passes

$r\quad =\sqrt { { (2-5) }^{ 2 }+{ (-3-0) }^{ 2 } } =\sqrt { 9+9 } =3\sqrt { 2 }$

$Area\quad =\quad \pi { r }^{ 2 }\quad =\quad \pi { (3\sqrt { 2 } ) }^{ 2 }=18\pi$

Radius of the circle = distance between the center and the point through which the circle passes

$r\quad =\sqrt { { (2-5) }^{ 2 }+{ (-3-0) }^{ 2 } } =\sqrt { 9+9 } =3\sqrt { 2 }$

$Area\quad =\quad \pi { r }^{ 2 }\quad =\quad \pi { (3\sqrt { 2 } ) }^{ 2 }=18\pi$