Question 384718
Use the point-slope form of a line, {{{y-y[p]=m(x-x[p])}}}.
{{{y-0=t(x-t)}}}
{{{y=tx-t^2}}}
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Now use the point (5,6),
{{{6=t*5-t^2}}}
{{{t^2-5t+6=0}}}
{{{(t-3)(t-2)=0}}}
Two solutions:
{{{t-3=0}}}
{{{t=3}}}
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{{{t-2=0}}}
{{{t=2}}}
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{{{drawing(300,300,-2,8,-2,8,grid(1),circle(5,6,0.2),graph(300,300,-2,8,-2,8,0,2(x-2),3(x-3)))}}}
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Ahmad, I tried to respond to your question but I got a bounceback. Hopefully you'll look here.

The answer is no.
{{{ t^2-6t-t+6=t^2-7t+6}}} and 
{{{ t^2-6t-t+6<>t^2-5t+6}}}
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I made the same mistake in my first solution, then went back to verify and caught the mistake.

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{{{t^2-5t+6=t^2-3t-2t+6}}}
{{{t^2-5t+6=t(t-3)-2(t-3)}}}
{{{t^2-5t+6=(t-3)(t-2)}}}