Given Parametric equations: #x = 2(t)^2# and y = 4t how do you find the cartesian equation?

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Answer 1 · 2016-07-22T15:23:27

#y = pm 2 sqrt (2 x)#

First, isolate t in each expression

#x = 2 t^2 implies t^2 = x/2 qquad circ#

#y = 4t implies t = y/4, t^2 = y^2 / 16 qquad triangle#

Next, comparing #circ# and #triangle#

#t^2 = x/2 = y^2 /16 implies y^2 = 8x#

you might wish to simplify further as #y = pm sqrt(8x) = pm 2 sqrt (2 x)#

if #t>=0# it is more simply #y = 2 sqrt (2 x)#