Question 1152029
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            In my post,  I will solve part  (ii)  only.



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Start from the standard trigonometry identity

    {{{1/(tan^2(theta)+1)}}} = {{{cos^2(theta)}}}.            (1)



From the given part of  (ii),  

    {{{tan(theta)}}} = {{{x/a}}}  and  {{{cos(theta)}}} = {{{y/b}}}.     (2)



Now replace in (1)  {{{tan(theta)}}}  by  {{{x/a}}}  and  replace  {{{cos(theta)}}}  by  {{{y/b}}},  based on (2).  You will get


    {{{1/((x/a)^2+1)}}} = {{{(y/b)^2}}}.                 (3)


Thus we just eliminated  {{{theta}}}  and obtained  the relationship  (the equation) for x and y.


The goal is reached:  the problem is just solved in this way.


You may simplify the equality  (4)  further as you want.
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