Chapter 11, Problem 1RCC

a.

To determine

To state: the definition of parabola.

Explanation of Solution

Given information:

The term ‘parabola’.

An open plane curve which is symmetrical in nature and is formed by the intersection of a cone with a plane parallel to its side is known as parabola. When a quadratic function is graphed, it forms a parabola, a u-shaped curve that has to meet certain technical mathematical requirements. A narrow curve at the end of an oval can be imagined as a parabola.

b.

To determine

To draw: the parabola $x^2=4py$ .

Explanation of Solution

Given information:

The parabola is $x^2=4py$ .

Graph: to graph the parabola, the graph of parabola is about the $y$ -axis.

The graph of parabola can be obtained as:

  Interpretation: form the above graph it can be observed that the vertex of the parabola is $\left(0,0\right)$ , focus is $\left(0,p\right)$ and directrix is $y=-p$ .

b.

To determine

To draw: the parabola $y^2=4px$ .

Explanation of Solution

Given information:

The parabola is $y^2=4px$ .

Graph: to graph the parabola, the graph of parabola is about the $y$ -axis.

The graph of parabola can be obtained as:

  Interpretation: form the above graph it can be observed that the vertex of the parabola is $\left(0,0\right)$ , focus is $\left(p,0\right)$ and directrix is $x=-p$ .