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Parametric equations of lines. It is often difficult to compose an equation of a line in the plane in Cartesian coordinates, in the form . - раздел Образование, Ne ...
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y
0 х
In such cases, a new parameter t is introduced, and the coordinates x,y of each point of the line are expressed in terms of t as
This is a parametric equation of a line. Eliminating the parameter t from this system of equations, we can obtain a general equation of the line.
Example. Write a parametric equation of a circle.
у
М(х;у)
R
t y
0 x x
Take the angle between the radius ОМ of any point and the x-axis for the parameter t and express the legs of the right-angled triangle in terms of the radius R and the angle t:
; ,
expressing x, y, we obtain a parametric equation of the circle:
Let us show how to obtain the general equation from the parametric equation by eliminating the parameter t.
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The distance between two points Let us find the distance between two points М and М in the plane... Example Find the distance between the two points А and... Using the above formula we obtain...
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