Tulnene sthitishil avasthet kahi prachal ghatak badalle tr kashach abhays yeto?
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parametric equation
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When the equation of a curve is written in such a way that the x , y and z coordinates of a point on the curve are expressed as a function of some other variable t , then such an equation is called a parametric equation and t is called a parameter. parameter) is called. When parameter as often parameter then defines an angle θ is used.
for example,
is the equation of a circle whose center is at (0, 0) and radius is 1.
Parametric equation is not actually a single equation but a set of many equations. Any straight line or curve can be written as a parameter equation. It is also noteworthy that Prach
can be selected in a variety of ways and it is good to choose a parameter that makes the equations look simple and easy to calculate.
three dimensional helix
There are some geometric curves which are very difficult to express in Cartesian coordinates but are very easily expressed in the form of parameterized equations:
Similarly, a torus with major radius R and minor radius r can be expressed simply by the following parameter equations:
Converting parameter equations into one equation
For this the parameter has to be eliminated .
Category :coordinate geometry
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parametric equation
The free encyclopedia from Wikipedia
Jump to navigationJump to search
When the equation of a curve is written in such a way that the x , y and z coordinates of a point on the curve are expressed as a function of some other variable t , then such an equation is called a parametric equation and t is called a parameter. parameter) is called. When parameter as often parameter then defines an angle θ is used.
for example,
Parametric equation is not actually a single equation but a set of many equations. Any straight line or curve can be written as a parameter equation. It is also noteworthy that Prach
{\displaystyle x=r\cos(t)}{\displaystyle x=r\cos(t)}
{\displaystyle y=r\sin(t)}{\displaystyle y=r\sin(t)}
Parametric Equation of Ellipse :
{\displaystyle x=a\,\cos t}{\displaystyle x=a\,\cos t}
{\displaystyle y=b\,\sin t}{\displaystyle y=b\,\sin t}
Where {\displaystyle 0\leq t<2\pi }{\displaystyle 0\leq t<2\pi } There are limits to the parameter.
Similarly, a torus with major radius R and minor radius r can be expressed simply by the following parameter equations:
'Torus' with r=2 i and r=1/2
{\displaystyle x=\cos(t)(R+r\cos(u))\;}{\displaystyle x=\cos(t)(R+r\cos(u))\;}
{\displaystyle y=\sin(t)(R+r\cos(u))\;}{\displaystyle y=\sin(t)(R+r\cos(u))\;}
{\displaystyle z=r\sin(u)\;,}{\displaystyle z=r\sin(u)\;,}
And {\displaystyle t\in [0,2\pi ),}{\displaystyle t\in [0,2\pi ),} {\displaystyle u\in [0,2\pi ).}{\displaystyle u\in [0,2\pi ).}
Converting parameter equations into one equation
For this the parameter has to be eliminated .
Category :coordinate geometry
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