Question Type 2: Tangents to implicitly defined curves Bootcamps

Find the equation of the tangent line to the curve $x^2 + y^2 = 2$ at the point $(1,1)$.

Find the equation of the tangent line to the curve $x^3 + y^3 = 2$ at the point $(1,1)$.

Find the equation of the tangent line to the curve $\ln(x) + \ln(y) = 0$ at the point $(1,1)$.

Find the equation of the tangent line to the curve $xy + y^2 = 2$ at the point $(1,1)$.

Find the equation of the tangent line to the curve $x^2y - y^2 = 0$ at the point $(1,1)$.

Find the equation of the tangent line to the curve $e^x + e^y = 2e$ at the point $(1,1)$.

Find the equation of the tangent line to the curve $\ln(xy) = 0$ at the point $(1,1)$.

Find the equation of the tangent line to the curve $x^2 + y^2 + xy = 3$ at the point $(1,1)$.

Find the equation of the tangent line to the curve $\arctan\bigl(\tfrac{y}{x}\bigr) = \tfrac{\pi}{4}$ at the point $(1,1)$.

Find the equation of the tangent line to the curve $e^x + xy = e + 1$ at the point $(1,1)$.

Find the equation of the tangent line to the curve $\sin(xy) = \sin(1)$ at the point $(1,1)$.

Find the equation of the tangent line to the curve $y^2 = x + \sin(x) - \sin(1)$ at the point $(1,1)$.