Identify the conic as a circle or an ellipse then find the radius.
$\frac { x ^ { 2 } } { 36 / 49 } + \frac { ( y + 1 ) ^ { 2 } } { 36 / 49 } = 1$
A) Ellipse
Center: $\frac { 6 } { 7 }$
B) Circle
Radius: $\frac { 6 } { 7 }$
C) Circle
Radius: 1
D) Ellipse
Center: 1
E) None of the above

Question

Identify the conic as a circle or an ellipse then find the radius. 
$\frac { x ^ { 2 } } { 36 / 49 } + \frac { ( y + 1 ) ^ { 2 } } { 36 / 49 } = 1$ 
A) Ellipse
Center: $\frac { 6 } { 7 }$
B) Circle
Radius: $\frac { 6 } { 7 }$
C) Circle
Radius: 1
D) Ellipse
Center: 1
E) None of the above

Quizplus · Accepted Answer

This is a circle centered at the point (0, -1) with a radius of 6/7. The equation of a circle with center (h, k) and radius r is given by 
$(x-h)^2+(y-k)^2=r^2$
Here, h = 0, k = -1 and r = 6/7. 
Substituting these values, we get 
$x^{2}+\left(y+1\right)^{2}=\frac{36}{49}$
Multiplying both sides by 49/36, we get the given equation.

Identify the Conic as a Circle or an Ellipse Then x236/49+(y+1)236/49=1\frac { x ^ { 2 } } { 36 / 49 } + \frac { ( y + 1 ) ^ { 2 } } { 36 / 49 } = 136/49x2​+36/49(y+1)2​=1

Identify the Conic as a Circle or an Ellipse Then $\frac { x ^ { 2 } } { 36 / 49 } + \frac { ( y + 1 ) ^ { 2 } } { 36 / 49 } = 1$