Problem 72

Given information

Two perpendicular line Intersect on the -axis and are both tangent to the parabola 

Step-by-step explanation

Because   is an even function, symmetric about the -axis, two perpendicular lines that are both tangent to and intersect on the -axis must have slopes 1 and   That is, the slope 1 line must make a angle with the positive -axis, the slope line must make a angle with the negative -axis.

Find the point where  has a tangent slope of 

  

and the corresponding  -coordinate   

So the point is    and because of symmetry the point on the other side is where the tangent slope is