Eliminate the Parameter
-A circle: $x = 2 + 5 \cos t , y = 5 + 5 \sin t$
A) $\frac { ( x - 2 ) ^ { 2 } } { 25 } + \frac { ( y - 5 ) ^ { 2 } } { 25 } = 1$
B) $\frac { ( x + 2 ) ^ { 2 } } { 25 } + \frac { ( y + 5 ) ^ { 2 } } { 25 } = 1$
C) $\frac { ( x - 5 ) ^ { 2 } } { 25 } + \frac { ( y - 2 ) ^ { 2 } } { 25 } = 1$
D) $( x - 2 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 25$

Question

Quizplus · Accepted Answer

Using the trigonometric identities $\cos^2(t) + \sin^2(t) = 1$, we can eliminate the parameter $t$ by rearranging the given equations to $(x - 2)^2 = 25\cos^2(t)$ and $(y - 5)^2 = 25\sin^2(t)$. Adding these equations gives $\frac{(x - 2)^2}{25} + \frac{(y - 5)^2}{25} = \cos^2(t) + \sin^2(t) = 1$, which matches choice A.

Eliminate the Parameter -A Circle x=2+5cos⁡t,y=5+5sin⁡tx = 2 + 5 \cos t , y = 5 + 5 \sin tx=2+5cost,y=5+5sint

Eliminate the Parameter
-A Circle $x = 2 + 5 \cos t , y = 5 + 5 \sin t$