**Topic**

Let the parabola have the canonical equation \({y^2} = 2x\). Find the focus, the equation of the standard line of the parabola and draw that parabola.

**Solution method – See details**

Given a parabola with PTCT: \({y^2} = 2px\) where \(p > 0\)

+ Focus: \(F\left( {\frac{p}{2};0} \right)\)

+ Standard curve: \(\Delta 😡 = – \frac{p}{2}\)

**Detailed explanation**

+ We have: \(2p = 2 \Rightarrow p = 1\)

The focus of the parabola (P) is \(F\left( {\frac{1}{2};0} \right)\)

Standard curve: \(\Delta 😡 = – \frac{1}{2}\)

+ Draw parabola

To draw a parabola (P): \({y^2} = 2x\) we can do the following:

Step 1: Make a table of values

x |
0 |
0.5 |
0.5 |
2 |
2 |
4.5 |
4.5 |

y |
0 |
-first |
first |
-2 |
2 |
-3 |
3 |

Note that for every positive value of x there are two opposite values of y

Step 2: Draw specific points where the coordinates and coordinates are defined as shown in the table of values

Step 3: Draw a parabola to the right of the Oy axis, the O vertex, the Ox symmetry axis, the parabola passing through the points drawn in Step 2