Question 1083798
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X = {{{a*sec(theta)}}},  Y = {{{b*tan(theta)}}}   ====>

X = {{{a/cos(theta)}}},  Y = {{{b*tan(theta)}}}   ====>

{{{X/a}}} = {{{1/cos(theta)}}},  {{{Y/b}}} = {{{tan(theta)}}}  ====>

{{{(X/a)^2}}} = {{{1/cos^2(theta)}}},  {{{Y/b)^2}}} = {{{sin^2(theta)/cos^2(theta)}}}  ====>

{{{X^2/a^2}}} - {{{Y^2/b^2}}} = {{{1/cos^2(theta)}}} - {{{sin^2(theta)/cos^2(theta)}}} = 1.


So, X and Y are constrained by the equation

{{{X^2/a^2}}} - {{{Y^2/b^2}}} = 1,

which is an equation of hyperbola.
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