Step-by-step explanation:
I've used elimination method over here but it can also be done by using substitution.
Answer:
![x^2 + y^2 + 4x + 4y = -119/16](https://tex.z-dn.net/?f=x%5E2%20%2B%20y%5E2%20%2B%204x%20%2B%204y%20%20%3D%20-119%2F16)
Step-by-step explanation:
The axes x and y are calibrated in 0.25
If the circle is carefully considered, the radius r of the circle is:
r = -1.25 - (-2)
r = 0.75 units
The equation of a circle is given by:
![(x - a)^2 + (y - b)^2 = r^2](https://tex.z-dn.net/?f=%28x%20-%20a%29%5E2%20%2B%20%28y%20-%20b%29%5E2%20%3D%20r%5E2)
The center of the circle (a, b) = (-2, -2)
Substituting (a, b) = (-2, -2) and r = 0.75 into the given equation:
![(x - (-2))^2 + (y - (-2))^2 = (3/4)^2\\\\(x + 2)^2 + (y + 2)^2 = (3/4)^2\\\\x^2 + 4x + 4 + y^2 + 4y + 4 = 9/16\\\\x^2 + y^2 + 4x + 4y + 8 = 9/16\\\\16x^2 + 16y^2 + 64x + 64y + 128 = 9\\\\16x^2 + 16y^2 + 64x + 64y = -119\\\\x^2 + y^2 + 4x + 4y = -119/16\\](https://tex.z-dn.net/?f=%28x%20-%20%28-2%29%29%5E2%20%2B%20%28y%20-%20%28-2%29%29%5E2%20%3D%20%283%2F4%29%5E2%5C%5C%5C%5C%28x%20%2B%202%29%5E2%20%2B%20%28y%20%2B%202%29%5E2%20%3D%20%283%2F4%29%5E2%5C%5C%5C%5Cx%5E2%20%2B%204x%20%2B%204%20%2B%20y%5E2%20%2B%204y%20%2B%204%20%3D%209%2F16%5C%5C%5C%5Cx%5E2%20%2B%20y%5E2%20%2B%204x%20%2B%204y%20%2B%208%20%3D%209%2F16%5C%5C%5C%5C16x%5E2%20%2B%2016y%5E2%20%2B%2064x%20%2B%2064y%20%2B%20128%20%3D%209%5C%5C%5C%5C16x%5E2%20%2B%2016y%5E2%20%2B%2064x%20%2B%2064y%20%20%3D%20-119%5C%5C%5C%5Cx%5E2%20%2B%20y%5E2%20%2B%204x%20%2B%204y%20%20%3D%20-119%2F16%5C%5C)
The second relation is a function.
For a relation to be a function, each x-value can only have a singular corresponding y-value. Since all other relations feature x-values with multiple y-values, the second relation is a function.