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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



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