A curve C in E[sub]3 [/sub]is the locus of point ([i]x,y,z[/i]) whose Cartesian coordinates[i] x,y,z[/i] are function of single parameter [i]t[/i].  A curve in space in parametric form is given by the equations[br]                [i]x=f(t), y=g(t), z=h(t)[/i]   [br][br]In the parametric form, a space curve s defined as locus of a point whose Cartesian coordinates x,y,z are function of single parameter. [br]In the parametric form, equation of space curve is given by[br]      [img 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                                       ......................(1)[br]The equation given in (1) is called explicit form or parametric form of space curve.[br]For example, [br]      [img 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is a space curve.[br][br][br]१। यसपछिको GeoGebra Applet मा तपाईहरुले parametric equation change गर्न सक्नुहुन्छ । जस्तै, [br] x=1+t भएको ठाउमा 1-t वा अरु कुनै t को expression लेख्न सक्नुहुन्छ ।[br][br]२। Point P=(x,y,z) मा check/un-check गरेर 3D graph मा point लाई locate गर्न सक्नुहुन्छ।[br][br]३। Animate point P मा Click गरेर Point P को motion हेर्न सक्नुहुन्छ। र Stop मा Click गरेर Point P को motion [br] लाई stop गर्न सक्नुहुन्छ।                                                                  

Input the value of x,y,and z in the applet above. Based on the output, answer the questions given below.[br]1. [math]\text{x= cost, y= sint, z= t/5}[/math][br]2. [math]\text{x= t cost, y= t sint, z= t}[/math][br]3. [math]\text{x= t^2, y=t^2+3, z= t^2-1}[/math][br]4. [math]x=2sint,y=0,z=2cost[/math]