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3 answers

True or False: The plane curve given by the parametric equations x = 3t + 4, y = 5t - 6 is a parabola.

False.

x = 3t + 4
y = 5t - 6

5x - 3y = 5(3t + 4) - 3(5t - 6) = 15t + 20 - 15t + 18
5x - 3y = 38

This is the equation of a line.

2007-06-11 20:50:35 · answer #1 · answered by Northstar 7 · 0 0

It is false...here's why...take the equation x=3t+4 and solve for t:
x=3t+4
x-4=3t
(x-4)/3=t

now subsitute this into y=5t-6 and simplify
y=5[(x-4)/3)]-6
since the question was is this a parabola, the answer is no because there is no x^2 term in the equation. With further simplification the equation becomes:
y=(5/3)x -38/3
which is the equation of a line...

2007-06-11 14:53:22 · answer #2 · answered by Stop Sine 3 · 1 0

no, since dy/dt = 5, dx/dt=3, hence dy/dx= 5/3 = const

2007-06-11 15:03:27 · answer #3 · answered by Anonymous · 1 0

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