Since you have found dy/dx, you are almost there you just have to find the y values
What you have to do is to substitute x=1 into y^2 - xy + x^2 = 7 and solve the quadratic equation. Then you will get two values for y. Which will be y = 3 or y = -2
All you have to do is to substitute y = 3, x = 1 into dy/dx and find the gradient and find the equation of the line.
Subsequently you can also substitute y = -2, x = 1 into dy/dx and find the gradient and find the equation of the line.
Just do one as the question requires to find only one equation of the line.
Hope it helps.