Find the equations of tangent and normal to the curve x3 + y3 - 9xy = | Basic Mathematics 2078

Basic Mathematics20785 marksNumerical: tangent and normal linesTangent and normal lines to curves

Find the equations of tangent and normal to the curve $x^3 + y^3 - 9xy = 0$ at the point $(2, 4)$ . [5]

Find the equations of tangent and normal to the curve $x^3 + y^3 - 9xy = 0$ at the point $(2, 4)$. [5]

Curve: $x^3 + y^3 - 9xy = 0$ - Point: $(2, 4)$ $2^3 + 4^3 - 9(2)(4) = 8 + 64 - 72 = 0 \checkmark$ $3x^2 + 3y^2\frac{dy}{dx} - 9\left(y + x\frac{dy}{dx}\right) = 0$ $\frac{dy}{dx}(3y^2 - 9x) = 9y - 3x^2$ $\frac{dy}{dx} = \frac{9y - 3x^2}{3y^2 - 9x} = \frac{3y - x^2}{y^2 - 3x}$ $$m = \fra...

Curve: $x^3 + y^3 - 9xy = 0$ - Point: $(2, 4)$ $$2^3 + 4^3 - 9(2)(4) = 8 + 64 - 72 = 0 \checkmark$$ $$3x^2 + 3y^2\frac{dy}{dx} - 9\left(y + x\frac{dy}{dx}\right) = 0$$ $$\frac{dy}{dx}(3y^2 - 9x) = 9y - 3x^2$$ $$\frac{dy}{dx} = \frac{9y - 3x^2}{3y^2 - 9x} = \frac{3y - x^2}{y^2 - 3x}$$ $$m = \fra...

Find the equations of tangent and normal to the curve x3 + y3 - 9xy = 0 at the point (2, 4).