At what point does the normal to y=0−1x−1x2 at (1,−2) intersect the parabola a second time?

Question

tkhunny · Answer

Have you considered writing the equation of the Normal Line?

anonymous · Answer

??

tkhunny · Answer

You cannot solve this problem if you do not know what  Normal Line is.  It is related to the Tangent Line.  Can you find its equation?  We have a point, (1,-2).  All we need is a slope.

anonymous · Answer

The normal line is perpendicular to the tangent line. If two lines are perpendicular their slopes are negative reciprocals -- i.e. if the slope of the first line is m then the slope of the second line is −1/m

tkhunny · Answer

Okay, what is the slope of the tangent lines at (1,-2)?

anonymous · Answer

-1

tkhunny · Answer

y= −x − x^2 at (1,−2) 

y' = -1 - 2x

y'(1) = -1 - 2(1) = -3 -- This is the slope of the tangent line through (1,-2).

-3(1/3) = -1

1/3 is the slope of the Normal Line through (1,-2)

Where did you get -1?  You didn't say what that was supposed to be, so it could have been anything.  Not really clear where it came from.