[ad_1]
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
[ad_2]
Source link net do edu
