Question

Dada a reta na forma paramétrica x = 3t - 2 e y = 2t + 1, eliminar t.

Answer 1

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$\large\begin{array}{l} \textsf{Para eliminar o par\^ametro t, isole o par\^ametro nas duas}\\\textsf{equ\c{c}\~oes param\'etricas e iguale:}\\\\ \left\{\!\begin{array}{lc} \mathsf{x=3t-2}&\quad\mathsf{(i)}\\\\ \mathsf{y=2t+1}&\quad\mathsf{(ii)} \end{array} \right. \end{array}$


$\large\begin{array}{l} \textsf{Por (i), temos}\\\\ \mathsf{3t=x+2}\\\\ \mathsf{t=\dfrac{x+2}{3}}\\\\\\ \textsf{Por (ii), temos}\\\\ \mathsf{2t=y-1}\\\\ \mathsf{t=\dfrac{y-1}{2}} \end{array}$


$\large\begin{array}{l} \textsf{Igualando,}\\\\ \mathsf{\dfrac{x+2}{3}=\dfrac{y-1}{2}}\\\\ \mathsf{2(x+2)=3(y-1)}\\\\ \mathsf{2x+4=3y-3}\\\\ \mathsf{2x+4-3y+3=0}\\\\ \boxed{\begin{array}{c} \mathsf{2x-3y+7=0} \end{array}}\quad\longleftarrow\quad\textsf{equa\c{c}\~ao geral.} \end{array}$


$\large\begin{array}{l} \textsf{D\'uvidas? Comente.}\\\\\\ \textsf{Bons estudos! :-)} \end{array}$


Tags: equação paramétrica da reta eliminar parâmetro geometria analítica álgebra