Identify the conic as a circle or an ellipse then find the radius. $$\frac { x ^ { 2 } } { 4 / 9 } + \frac { ( y + 1 ) ^ { 2 } } { 4 / 9 } = 1$$
A) Ellipse
Center: 1
B) Circle
Radius: $\frac { 2 } { 3 }$
C) Circle
Radius: 1
D) Ellipse
Center: $\frac { 2 } { 3 }$
E) None of the above

Question

Identify the conic as a circle or an ellipse then find the radius. $$\frac { x ^ { 2 } } { 4 / 9 } + \frac { ( y + 1 ) ^ { 2 } } { 4 / 9 } = 1$$ 
A) Ellipse
Center: 1
B) Circle
Radius: $\frac { 2 } { 3 }$
C) Circle
Radius: 1
D) Ellipse
Center: $\frac { 2 } { 3 }$
E) None of the above

Quizplus · Accepted Answer

The given equation can be rewritten as $\frac{(x-0)^2}{(\frac{2}{3})^2}+\frac{(y+1-0)^2}{(\frac{2}{3})^2}=1$, which is the standard form equation of a circle centered at $(0,-1)$ with radius $\frac{2}{3}$. Therefore, the answer is (B) Circle, Radius: $\frac{2}{3}$.

Identify the Conic as a Circle or an Ellipse Then x24/9+(y+1)24/9=1\frac { x ^ { 2 } } { 4 / 9 } + \frac { ( y + 1 ) ^ { 2 } } { 4 / 9 } = 14/9x2​+4/9(y+1)2​=1

Identify the Conic as a Circle or an Ellipse Then $\frac { x ^ { 2 } } { 4 / 9 } + \frac { ( y + 1 ) ^ { 2 } } { 4 / 9 } = 1$