The left semicircle centered at (0, 0) with radius 4
A) $x = \sqrt { 4 - y ^ { 2 } }$
B) $x = \sqrt { 16 - y ^ { 2 } }$
C) $x = - \sqrt { 4 - y ^ { 2 } }$
D) $x = - \sqrt { 16 - y ^ { 2 } }$

Question

The left semicircle centered at (0, 0) with radius 4 
A) $x = \sqrt { 4 - y ^ { 2 } }$
B) $x = \sqrt { 16 - y ^ { 2 } }$
C) $x = - \sqrt { 4 - y ^ { 2 } }$
D) $x = - \sqrt { 16 - y ^ { 2 } }$

Quizplus · Accepted Answer

The equation of a circle centered at (0,0) with radius 4 is $x^2 + y^2 = 16$. Solving for $x$ to represent the left semicircle, we get $x = -\sqrt{16 - y^2}$, as this ensures $x$ is negative, corresponding to the left side of the y-axis.

The Left Semicircle Centered at (0, 0) with Radius 4 x=4−y2x = \sqrt { 4 - y ^ { 2 } }x=4−y2​

The Left Semicircle Centered at (0, 0) with Radius 4 $x = \sqrt { 4 - y ^ { 2 } }$