is it possible to make y the subject in x^2-xy+y^2=1???

wat

Yes, using the same way the quadratic formula is derived. Isolate the y terms:

y^2 - xy = 1 - x^2

Complete the square by halving the coefficient of -xy (-x/2), squaring it (x^2/4) and then adding it to both sides:

y^2 - xy + x^2/4 = 1 - 3x^2/4

Factor the left side and combine the fractions on the right:

(y - x/2)^2 = (4 - 3x^2) / 4

Square root both sides:

y - x/2 = +- sqrt(4 - 3x^2) / 2

Add x/2 to both sides:

y = [x +- sqrt(4 - 3x^2)] / 2

That means can you solve the equation for y, so yes.

Consider x as a constant and solve the quadratic equation in y that results.

Thus y^2 - xy + x^2 - 1 = 0,

So y = (x +/- sqrt(x^2 - 4(x^2-1)) / 2,

So y = (x +/- sqrt(4-3x^2) } / 2.

x² − xy + y² = 1

y² − xy + (x²−1) = 0

Using quadratic formula: y = (−b ± √(b²−4ac)) / (2a)

where a = 1, b = −x, c = x²−1

y = (x ± √(x²−4(x²−1))) / 2

y = (x ± √(4−3x²)) / 2

Do implicit differentiation, in the end(althoiugh I won't solve it for you), you will get something along the lines of dy/dx=something. I woudl Isolate Y to one side divide, cross multiply whatever. I take calclus, taht would be my approach.

I think the best answer selected is really the best ....

yes its possible.