Question 1191548

1. {{{x^2+(y-5)^2=25}}}


In polar coordinates, {{{x = r*cos(theta )}}} and {{{y=r*sin(theta)}}}.


Thus, the input can be rewritten as 


{{{(r *cos(theta ))^2+(r*sin(theta)-5)^2=25}}}


{{{r^2 *cos^2(theta )+r^2*sin^2(theta)-2*5r*sin(theta)+25=25}}}


{{{r^2 (cos^2(theta )+sin^2(theta))-10r*sin(theta)=25-25}}}


{{{r^2 (1)-10r*sin(theta)=0}}}


{{{r^2=10r*sin(theta)}}}


{{{r=10sin(theta)}}}



2.


{{{5x - 2y=1}}}


 {{{x = r *cos(theta ) }}}and {{{y=r*sin(theta)}}}


{{{5r *cos(theta )  - 2r*sin(theta)=1}}}


{{{r (5cos(theta )  - 2sin(theta))=1}}}


{{{r =1/(5cos(theta )  - 2sin(theta))}}}