Parametric Equation Help!

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1

<p>Hey, could someone please show me how to solve this:</p>

<p>"The graph of xy - 4x - 2y - 4 = 0 can be expressed as a set of parametric equations. If y = (4t)/(t - 3) and x = f(t), then f(t) ="</p>

<p>I know I have to substitute y in the equation and simply get x = t - 1, but I've spent the last half hour trying to see how it simplifies to 12x - 12t + 12 = 0 but still haven't figured it out.</p>

<p>Please show me how you can simplify the equation x((4t)/(t - 3)) - 4x - 2((4t)/(t - 3)) - 4 = 0</p>

<p>Thanks!</p>

2

<p>I got it to simplify to “x - t +1 = 0”…</p>

3

<p>x((4t)/(t - 3)) - 4x - 2((4t)/(t - 3)) - 4 = 0
x((4t)/(t - 3)) - 2((4t)/(t - 3)) = 4 + 4x
(4xt)/(t - 3) - (8t)/(t - 3) = 4 + 4x
(4xt - 8t)/(t - 3) = 4 + 4x
4xt - 8t = (t - 3)*(4 + 4x)
4xt - 8t = 4t + 4xt -12 - 12x

  • 8t = 4t - 12 - 12x
    -12t = -12 - 12x
    12x + 12 - 12t = 0
    x - t + 1 = 0</p>
4

<p>Thank you so much! I have no idea why I was having trouble with that, sometimes I just completely mess up! Thanks again :D</p>

5

<p>my answer says that f(t) = t+1
HOW??</p>

6

<p>A slightly easier way to solve it:</p>

<p>Solve for x in terms of y:
xy - 4x = 2y + 4 → x(y-4) = 2y + 4</p>

<p>x = (2y + 4)/(y-4) = 2 + 12/(y-4) (I simply rewrote 2y + 4 as 2y - 8 + 12, simplified)</p>

<p>Since y = 4t/(t-3), y-4 = 4t/(t-3) - 4 = 12/(t-3). Substituting into our expression for x,</p>

<p>x = 2 + 12/(12/(t-3)) = 2 + (t-3) = t-1.</p>

<p>Therefore x = f(t) = t-1.</p>