If a curve passes through the origin and the slope
Question:

If a curve passes through the origin and the slope of the tangent to it at any point $(x, y)$ is $\frac{x^{2}-4 x+y+8}{x-2}$, then this curve also passes through the point:

  1. (1) $(4,5)$

  2. (2) $(5,4)$

  3. (3) $(4,4)$

  4. (4) $(5,5)$


Correct Option: , 4

Solution:

$\frac{d y}{d x}=\frac{(x-2)^{2}+y+4}{(x-2)}=(x-2)+\frac{y+4}{(x-2)}$

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