Chapter 8.2, Problem 2E

Solution

To explain : The comparison between the graphs of $x^2=4py$ and $y^2=4px$ .

The differences in the graphs of $x^2=4py$ and $y^2=4px$ are in the opening of the parabola, focus, directrix and axis of symmetry.

Given information :

The equations $x^2=4py$ and $y^2=4px$ .

Explanation :

Consider the graph of the equation $x^2=4py$ when $p>0$ .

  

Consider the graph of the equation $x^2=4py$ when $p<0$ .

  

The parabola of the equation $x^2=4py$ opens either upward or downward. The focus is $\left(0,p\right)$ , directrix is $y=-p$ and axis of symmetry is vertical.

Consider the graph of the equation $y^2=4px$ when $p>0$ .

  

Consider the graph of the equation $y^2=4px$ when $p<0$ .

  

The parabola of the equation $x^2=4py$ opens either left or right. The focus is $\left(p,0\right)$ , directrix is $x=-p$ and axis of symmetry is horizontal.

Therefore, the differences in the graphs of $x^2=4py$ and $y^2=4px$ are in the opening of the parabola, focus, directrix and axis of symmetry.