For the following parametric equations, eliminate the parameter to give Cartesian equation in x and y.
x = a sec t , y = b tan t
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My working so far...
x = a sec t ----1
y = b tan t ----2
From 1: x = a sec t
x/a = sec t
From 2: y = b tan t
y/b = tan t
Using sec^2 - tan^2 = 1
(x/a)^2-(y/b)^2 = 1
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Please teach me how to continue please ~ Very thanks.
x = a sec t , y = b tan t
______________________________________…
My working so far...
x = a sec t ----1
y = b tan t ----2
From 1: x = a sec t
x/a = sec t
From 2: y = b tan t
y/b = tan t
Using sec^2 - tan^2 = 1
(x/a)^2-(y/b)^2 = 1
______________________________________…
Please teach me how to continue please ~ Very thanks.
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Why do you need to continue? You have the equation in Cartesian coordinates for a hyperbola with its two arms centred on the Cartesian origin and its transverse axis aligned along the Cartesian x-axis. What more can you ask for?!
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sect=x/a, tant=y/b sec^2t-tan^2t=1 x^2/a^2-y^2/b^2=1