Answer:
The curve produces a slope field with vertical tangents at y = 2.
Step-by-step explanation:
The differential equation [tex]\frac{dy}{dx}[/tex] equals the quotient of the quantity x minus 2 and y minus 2.
Hence, [tex]\frac{dy}{dx} = \frac{x - 2}{y - 2}[/tex]
Now, at y = 2, [tex]\frac{dy}{dx}[/tex] becomes ∞ and hence the curve y = f(x) with [tex]\frac{dy}{dx} = \frac{x - 2}{y - 2}[/tex] will have tangents at y = 0 with slopes equal to ∞ i.e. the tangents make 90° angle with the positive x-axis.
Therefore, the curve produces a slope field with vertical tangents at y = 2. (Answer)
