Answer
The equations $x^{2} + y^{2} = 1$ and $x^{2} + y^{2}=4$ are equations of a circle satisfying the center-radius form: $$(x – h)^{2} + (y – k)^{2} = r^{2}$$
From this equation, we know that the center will lie at point $(h,k)$, which in this case will both be at point $(0,0)$.
Since both have the same center and different radius, the plots of these equations will never intersect, as one circle $(r = 2)$ will circumscribe the other $(r = 1)$.
Work Step by Step
The equations $x^{2} + y^{2} = 1$ and $x^{2} + y^{2}=4$ are equations of a circle satisfying the center-radius form: $$(x – h)^{2} + (y – k)^{2} = r^{2}$$
From this equation, we know that the center will lie at point $(h,k)$, which in this case will both be at point $(0,0)$.
Since both have the same center and different radius, the plots of these equations will never intersect, as one circle $(r = 2)$ will circumscribe the other $(r = 1)$.
