In a nuclear fusion experiment, the magnetic flux boundary in a specific cross-section of the tokamak is modeled by the implicit equation
2x2y−3y2+x3=12 2x^2y - 3y^2 + x^3 = 12 2x2y−3y2+x3=12where x x\,x and y y\,y are spatial coordinates in decimeters.
Determine the equation of the tangent line to this boundary at the point P(2,2)P(2, 2)P(2,2), expressing your result in the form ax+by+c=0ax + by + c = 0ax+by+c=0, where a,ba, ba,b, and c c\,c are integers.
649 exam-style questions on Edexcel A Level Maths Differentiation, covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change. Each one has a worked solution and a mark scheme showing where the marks go.