Question 183261
{{{(x-2)^2/16 + (y-1)^2/25 = 1}}} Start with the given equation.



{{{((x-2)/4)^2 + ((y-1)/5)^2 = 1}}} Rewrite {{{(x-2)^2/16}}} as {{{((x-2)/4)^2}}}. Rewrite {{{(y-1)^2/25}}} as {{{((y-1)/5)^2}}}



Now since {{{(cos(t))^2+(sin(t))^2=1}}} for all "t", this means that 



{{{(cos(t))^2+(sin(t))^2=((x-2)/4)^2 + ((y-1)/5)^2}}}



So {{{(cos(t))^2=((x-2)/4)^2}}} and {{{(sin(t))^2=((y-1)/5)^2}}}



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{{{(cos(t))^2=((x-2)/4)^2}}} Start with the first equation.



{{{cos(t)=(x-2)/4}}} Take the square root of both sides.



{{{4*cos(t)=x-2}}} Multiply both sides by 4.



{{{4*cos(t)+2=x}}} Add 2 to both sides.



So the first parametric equation is {{{x=4*cos(t)+2}}}



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{{{(sin(t))^2=((y-1)/5)^2}}} Start with the first equation.



{{{sin(t)=(y-1)/5}}} Take the square root of both sides.



{{{5*sin(t)=y-1}}} Multiply both sides by 5.



{{{5*sin(t)+1=y}}} Add 1 to both sides.



So the second parametric equation is {{{y=5*sin(t)+1}}}



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Answer:


So the parametric equations are: 


{{{x=4*cos(t)+2}}}
{{{y=5*sin(t)+1}}}