SOLUTION: Consider the curve y= 2/x with x>0. The normal to the curve at point P intersects the y axis at (0,-3). Find the point P? I understand the gradient of the normal is -2/x^2 and the

Question 364660: Consider the curve y= 2/x with x>0. The normal to the curve at point P intersects the y axis at (0,-3). Find the point P?
I understand the gradient of the normal is -2/x^2 and the equation using (0,-3)
making 2/x = -2/x^2-3 so -2/x^2-2/x-3 but can't think of where else to go

Note: At somepoint in the in solving this problem you may be required to solve a non trivial possibly high degree polynomial equation. in that case trial and error may be required but note that the answer should be a possitive integer smaller than 5
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
You can get the value of the slope of the tangent line for the curve by taking the derivative.

The tangent and the normal to the curve are perpendicular to each other.
PErpendicular lines have slopes that are negative reciprocals.

Now you have the slope of the normal line and you have one point (0,-3).
Use the point slope form of a line,

But you also know that,

Substitute,

Multiply both sides by ,

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That curve has a zero at
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P:(2,1)
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