Asked by Morgan Berryman on Mar 10, 2024

Verified

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

A) $(x−4)_{2}+(y−2)_{2}=4$

B) $(x+4)_{2}+(y+2)_{2}=16$

C) $(x+4)_{2}+(y+2)_{2}=4$

D) $(x−4)_{2}+(y−2)_{2}=16$

E) $(x+4)_{2}+(y−2)_{2}=4$

A) $(x−4)_{2}+(y−2)_{2}=4$

B) $(x+4)_{2}+(y+2)_{2}=16$

C) $(x+4)_{2}+(y+2)_{2}=4$

D) $(x−4)_{2}+(y−2)_{2}=16$

E) $(x+4)_{2}+(y−2)_{2}=4$

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.

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.

## Learning Objectives

- Refine proficiency in framing and detecting the standard depictions of equations of circles.