Question 1191359


Transform the following equation to a cartesian equation: 

{{{r=sec(theta)*tan^2(theta)}}}

First convert the expression into terms of {{{cos(theta) }}}and {{{sin(theta)}}}...............{{{sec(theta)=1/cos(theta) }}}and {{{tan^2(theta)=sin^2(theta)/cos^2(theta)}}}


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


{{{r=sin^2(theta)/cos^3(theta)}}}


{{{r*cos^3(theta)=sin^2(theta)}}}


Now the normal substitutions are: 

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


Substituting these values into the expression above gives


{{{r*(x/r)^3=(y/r)^2}}}

{{{r*(x^3/r^3)=y^2/r^2}}}

{{{x^3/r^2=y^2/r^2}}}

{{{x^3=y^2}}}