Question: The slope of the tangent to the curve $x^{2} + y^{2} = 2c^{2}$ at point (c, c) is...

Question

The slope of the tangent to the curve $x^{2} + y^{2} = 2c^{2}$ at point

(c, c) is

Answer 1

Given $x^{2} + y^{2} = 2c^{2}$

Differentiating w.r.t. x, $2x + 2y\frac{dy}{dx} = 0$

⇒ $2y\frac{dy}{dx} = - 2x$ ⇒ $\frac{dy}{dx} = \frac{- x}{y}$ ⇒ $\left( \frac{dy}{dx} \right)_{(c,c)} = - 1$

Question: The slope of the tangent to the curve \(x^{2} + y^{2} = 2c^{2}\) at point (c, c) is...