Thread: Normal to a parabola

Find the y intercept of the normal to the parabola at the points , where a does not equal to 0.
Find the limit of this y intercept as a approaches 0.
For each b >0 determine the number of normals that can be drawn from the point (0,b) to the parabola

Originally Posted by Dragon

Find the y intercept of the normal to the parabola at the points , where a does not equal to 0.

The "normal" is the perpendicular. So what is the "slope" of f(x) = x^2 at x = a? Then what is the slope of the perpendicular?

Use this slope and the given point to the line equation.

Then plug "0" in for "x" to find the y-intercept of this perpendicular line.

Originally Posted by Dragon

Find the limit of this y intercept as a approaches 0.

What expression do you get for the y-intercept? What limit do you get as a -> 0?

Originally Posted by Dragon

For each b >0 determine the number of normals that can be drawn from the point (0,b) to the parabola

What are your thoughts...?