Find two functions defined implicitly by the given relation.
-$$x ^ { 2 } + y ^ { 2 } = 81$$
A) $y = \sqrt { 81 } + x$ or $y = \sqrt { 81 } - x$
B) $y = \sqrt { 81 - x ^ { 2 } }$ or $y = \sqrt { 81 + x ^ { 2 } }$
C) $y = \sqrt { 81 } + x$ or $y = - \sqrt { 81 } - x$
D) $y = \sqrt { 81 - x ^ { 2 } }$ or $y = - \sqrt { 81 - x ^ { 2 } }$

Question

Quizplus · Accepted Answer

The given equation $x^2 + y^2 = 81$ represents a circle with a radius of 9 centered at the origin. Solving for $y$, we get $y = \pm\sqrt{81 - x^2}$, which corresponds to the upper and lower halves of the circle, respectively. Choices A, B, and C do not correctly represent the solutions for $y$ in terms of $x$ for the given circle equation.

Find Two Functions Defined Implicitly by the Given Relation x2+y2=81x ^ { 2 } + y ^ { 2 } = 81x2+y2=81

Find Two Functions Defined Implicitly by the Given Relation $x ^ { 2 } + y ^ { 2 } = 81$