Question

Tell what kind of graph this equation yields, and identify the domain and range.

4x^2+4y^2=16

Answer 1

are you familiar with circle equations?

Answer 2

Equation of a circle is
\[(x-a)^2+(y-b)^2=r^2\]
where (a,b) is the center of the circle and r is the radius so lets see the equation in the question shall we it is
\[4x^2+4y^2=16\]
we can also write this as
\[4(x-0)^2+4(y-0)^2=4^2\]
if we compare (a.b) it shows us that (a,b)-->(0,0) that is the origin so the center of the circle is an origin and radius is 4 if we simplify the equation lets say divide the equation by 4 we get
\[x^2+y^2=2^2\]
this means the radius is 2

Answer 3

let us sketch this