Answer:
The slope of the tangent m = -0.0833
Step-by-step explanation:
Step(i):-
Given that the curve
x y - 2y² + x² = -5 ...(i)
Differentiating equation (i) with respective to 'x', we get
[tex]x(\frac{dy}{dx} )+y (1) -2(2y)\frac{dy}{dx} + 2x=0[/tex]
[tex]x(\frac{dy}{dx} ) -2(2y)\frac{dy}{dx} = -2x-y[/tex]
[tex](x -4y)\frac{dy}{dx} = -2x-y[/tex]
[tex]\frac{dy}{dx} = \frac{-2x-y}{x-4y}[/tex]
Step(ii):-
The slope of the tangent
[tex](\frac{dy}{dx})_{1,-1.5} = \frac{-2x-y}{x-4y}[/tex]
[tex](\frac{dy}{dx})_{1,-1.5} = \frac{-2(1)-(-1.5)}{1-4(-1.5)}[/tex]
m = [tex]\frac{-2+1.5}{1+6}[/tex]
[tex]m = \frac{-0.5}{6} = -0.083[/tex]
The slope of the tangent m = -0.0833
