Write the corresponding rectangular equation for the curve represented by the parametric equations $x = 9 \cos \theta , y = 9 \sin \theta$
by eliminating the parameter.
A) $x ^ { 2 } + y ^ { 2 } = 18$
B) $x + y = 9$
C) $x + y = 18$
D) $x ^ { 2 } + y ^ { 2 } = 9$
E) $x ^ { 2 } + y ^ { 2 } = 81$

Question

Write the corresponding rectangular equation for the curve represented by the parametric equations $x = 9 \cos \theta , y = 9 \sin \theta$ 
by eliminating the parameter. 
A) $x ^ { 2 } + y ^ { 2 } = 18$
B) $x + y = 9$
C) $x + y = 18$
D) $x ^ { 2 } + y ^ { 2 } = 9$
E) $x ^ { 2 } + y ^ { 2 } = 81$

Quizplus · Accepted Answer

Using the Pythagorean identity $\cos^2\theta + \sin^2\theta = 1$, and substituting $x = 9\cos\theta$ and $y = 9\sin\theta$, we get $\frac{x^2}{81} + \frac{y^2}{81} = 1$, which simplifies to $x^2 + y^2 = 81$.

Write the Corresponding Rectangular Equation for the Curve Represented by the Parametric