Question

Equations x = 3 cost and y = 3 sint represent the equation of​

Answer 1

$\textbf{Given:}$

$x=3\,cost\;\text{and}\;y=3\,sint$

$\textbf{To find:}$

$\text{Cartesian form of given parametric equations}$

$\textbf{Solution:}$

$\text{Consider,}$

$x=3\,cost\;\text{and}\;y=3\,sint$

$\implies\,cost=\dfrac{x}{3}\;\text{and}\;sint=\dfrac{y}{3}$

$\text{We know that,}$

$cos^2t+sin^2t=1$

$(\dfrac{x}{3})^2+(\dfrac{y}{3})^2=1$

$\dfrac{x^2}{9}+\dfrac{y^2}{9}=1$

$\implies\,x^2+y^2=9$

$\implies\,x^2+y^2=3^2$

$\text{This is equation of a circle having centre at origin and radius 3}$

$\therefore\textbf{The given parametric equations represent a circle}$

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