Question

eliminate theta from the following x=7+3cos theta, y=5+3sin theta Plz give me ans.​

Answer 1

Step-by-step explanation:

x=7+3cosθ ----(1)

y=5+3sinθ ----(2)

by solving equation (1)

cosθ= (x-7)/3

square on both side:

cos^2θ= (x-7)^2/(3)^2

cos^2θ= (x^2 -14x +49)/9 ----(3)

by solving equation (2)

sinθ=(y-5)/3

square on both side:

sin^2θ=(y-5)^2/(3)^2

sin^2θ=(y^2 -10y +25)/9 ------(4)

adding equation (3) &(4)

sin^2θ+cos^2θ=(y^2 -10y +25)/9 + (x^2 -14x +49)/9

As we, sin^2θ+cos^2θ =1

so, 1 = (y^2 -10y +25)/9 + (x^2 -14x +49)/9

1 = 1/9[(y^2 -10y +25) + (x^2 -14x +49)]

9 = [y^2 -10y +25 + x^2 -14x +49]

9 = y^2 -10y + x^2 -14x + 74

0 = x^2 + y^2 -14x -10y+ 74-9

0 = x^2 + y^2 -14x -10y+ 65

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