Answer: 4π
Step-by-step explanation:
Under the assumption that those are exponents, and your equation is:
[tex]2x^2+2y^2=8[/tex]
You first must turn this circle equation into standard form. The standard form for the equation of a circle is as follows:
[tex](x-a)^2+(y-b)^2=r^2[/tex]
For your case, the constants 'a' and 'b' are clearly zero. We have an annoying coefficient of 2 which can be cancelled by dividing both sides by 2:
[tex]x^2+y^2=4[/tex]
If you'd like, we can write this in the following way:
[tex](x-0)^2+(y-0)^2=2^2[/tex]
So, our circle is centered at the origin (0, 0) and has a radius of 2 units. The area of a circle is given by the formula:
[tex]A=\pi r^2[/tex]
[tex]A=\pi (2^2)=4\pi[/tex]
