Write the equation for the shape described.
-The circle with endpoints of a diameter at $( - 1,4 )$ and $( - 1 , - 4 )$
A) $( x - 4 ) ^ { 2 } + y ^ { 2 } = 1$
B) $( x + 1 ) ^ { 2 } + y ^ { 2 } = 4$
C) $x ^ { 2 } + ( y - 4 ) ^ { 2 } = 1$
D) $( x + 1 ) ^ { 2 } + y ^ { 2 } = 16$

Question

Quizplus · Accepted Answer

The center of the circle is the midpoint of the diameter, which is $(-1, 0)$, and the radius is the distance from the center to either endpoint, which is 4. The equation of a circle is $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center and $r$ is the radius. Substituting $h = -1$, $k = 0$, and $r = 4$ gives $(x + 1)^2 + y^2 = 16$.

Write the Equation for the Shape Described (−1,4)( - 1,4 )(−1,4)

Write the Equation for the Shape Described $( - 1,4 )$