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For the curve defined by y(x−2)(x−3)=x+6, consider the point where it cuts the y-axis. The normal drawn to the curve at that point goes through which point?
- (1/2, 1/3)
- (−1/2, −1/2)
- (1/2, 1/2)
- (1/2, −1/3)
Correct answer: (1/2, 1/2)
Solution
At the y-axis x=0 gives 6y=6, so y=1. Differentiating y=(x+6)/(x^2-5x+6) gives dy/dx=1 at (0,1). The normal has slope -1: y-1=-(x-0), i.e. y=1-x, which passes through (1/2, 1/2).
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