## Solve Lesson 3 Page 67 Math Study Topic 10 – Kite>

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