Implicit function existence

Does the equation 2*(y-3)^2 +3*(x-2)^2 =20 define y as a differentiable implicit function of x or x as a differentiable implicit function of y or both or neither at the point (x,y) =(0,1)? Here, ln denotes the natural logarithm, ^ power, * multiplication, / division, + addition, - subtraction.

Select one:

a.

y is an implicit function of x but x is not an implicit function of y

b.

neither: y is not an implicit function of x and x is not an implicit function of y

c.

x is an implicit function of y but y is not an implicit function of x

d.

both: y is an implicit function of x and x is an implicit function of y