How do you transform parametric equations into Cartesian form: x= 3 + 2 cost and y= 1 + 5sint?

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Answer 1 · 2016-08-07T01:57:34

#25x^2+4y^2-150x-8y+129=0#

As #x=3+2cost# and #y=1+5sint#,

we have #cost=(x-3)/2# and #sint=(y-1)/5#

Hence #((x-3)/2)^2+((y-1)/5)^2=1# or

#(x^2-6x+9)/4+(y^2-2y+1)/25=1# or

#25(x^2-6x+9)+4(y^2-2y+1)=100# or

#25x^2+4y^2-150x-8y+225+4-100=0# or

#25x^2+4y^2-150x-8y+129=0#

graph{25x^2+4y^2-150x-8y+129=0 [-7.295, 12.705, -3.92, 6.08]}