Explanation

(a)
Given , $x^{2} - 2xy + y^{2} + 2x + y - 6 = 0$
On differentiating w.r.t.$x,$ we get
$2x - 2\left( y + x\frac{dy}{dx} \right) + 2y\frac{dy}{dx} + 2 + \frac{dy}{dx} = 0$
At (2,2)
$4 - 2\left( 2 + 2\frac{dy}{dx} \right) + 4\frac{dy}{dx} + 2 + \frac{dy}{dx} = 0$
$\Rightarrow \ \ \ \ \frac{dy}{dx} = - 2$
$\therefore\ \ \$Equation of tangent at (2,2) is
$(y - 2) = - 2(x - 2)$
$\Rightarrow \ \ \ 2x + y = 6$