Write the equation for the shape described.
-The upper semicircle centered at (0, 0) with radius 3
A) $y = - \sqrt { 9 - x ^ { 2 } }$
B) $y = \sqrt { 3 + x ^ { 2 } }$
C) $y = \sqrt { 3 - x ^ { 2 } }$
D) $y = \sqrt { 9 - x ^ { 2 } }$

Question

Write the equation for the shape described.
-The upper semicircle centered at (0, 0) with radius 3 
A) $y = - \sqrt { 9 - x ^ { 2 } }$
B) $y = \sqrt { 3 + x ^ { 2 } }$
C) $y = \sqrt { 3 - x ^ { 2 } }$
D) $y = \sqrt { 9 - x ^ { 2 } }$

Quizplus · Accepted Answer

The equation for a circle centered at (0, 0) with radius r is $x^2 + y^2 = r^2$. For a radius of 3, $r^2 = 9$, so the circle's equation is $x^2 + y^2 = 9$. Solving for $y$ to get the upper semicircle, we take the positive square root, resulting in $y = \sqrt{9 - x^2}$.

Write the Equation for the Shape Described y=−9−x2y = - \sqrt { 9 - x ^ { 2 } }y=−9−x2​

Write the Equation for the Shape Described $y = - \sqrt { 9 - x ^ { 2 } }$