If -xy+x=-5y^2-5 then find the equations of all tangent lines to the curve when x=-5. iimplicit derivative at a point

Answer 1

Find all y-values that correspond to x = -5:

5y - 5 = -5y² - 5 5y² + 5y = 0 5y(y + 1) = 0. y = 0 or -1

Differentiate implicitly w/ respect to x:

-y - x·dy/dx + 1 = -10y·dy/dx

(10y - x)·dy/dx = y - 1

dy/dx = (y - 1) / (10y - x) at (-5 , 0) dy/dx = -1/5. and at (-5 , -1) dy/dx = 2/5

y = -1/5(x + 5). and y + 1 = 2/5(x + 5)