# Thread: Normal to a parabola

1. ## Normal to a parabola

Find the y intercept of the normal to the parabola $\displaystyle y=x^2$ at the points $\displaystyle (a,a^2)$, 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 $\displaystyle y=x^2$

2. Originally Posted by Dragon
Find the y intercept of the normal to the parabola $\displaystyle y=x^2$ at the points $\displaystyle (a,a^2)$, 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 $\displaystyle y=x^2$