Asked by Morgan Berryman on Mar 10, 2024

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Write the standard form of the equation of the circle with the center at (4,2) that has radius 4.

A) (x−4) 2+(y−2) 2=4( x - 4 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 4(x4) 2+(y2) 2=4
B) (x+4) 2+(y+2) 2=16( x + 4 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 16(x+4) 2+(y+2) 2=16
C) (x+4) 2+(y+2) 2=4( x + 4 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = 4(x+4) 2+(y+2) 2=4
D) (x−4) 2+(y−2) 2=16( x - 4 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 16(x4) 2+(y2) 2=16
E) (x+4) 2+(y−2) 2=4( x + 4 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 4(x+4) 2+(y2) 2=4

Center

In geometry, the central point of a circle or sphere, equidistant from all points on the perimeter or surface.

Radius

A line segment from the center of a circle to any point on its circumference, or the length of this segment.

  • Refine proficiency in framing and detecting the standard depictions of equations of circles.
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Verified Answer

JR
Jesse Rubin

Mar 10, 2024

Final Answer :
D
Explanation :
The standard form of the equation of a circle with center $(h,k)$ and radius $r$ is $(x-h)^2+(y-k)^2=r^2$. Plugging in the values given, we get $(x-4)^2+(y-2)^2=4^2$, which simplifies to $(x-4)^2+(y-2)^2=16$. The correct choice is therefore D.