Rusty - fill in missing steps, please

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The discussion revolves around finding the gradient of the chord connecting two points on the parabola defined by the equations y^2 = 2x and x = (1/2)t^2, y = t. The user is struggling to understand how to derive the gradient formula m = (t1 - t2) / (0.5(t1^2 - t2^2)) = 2 / (t1 + t2). Participants clarify that the transition from the first to the second fraction involves recognizing the difference of squares formula, a^2 - b^2 = (a - b)(a + b). Additionally, there are discussions about the correct formatting of LaTeX for mathematical expressions. The conversation ultimately aids in reinforcing the understanding of both the gradient calculation and proper LaTeX syntax.
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Hello everyone,

I'm taking a high level Geometry course, and as it turns out, I'm a tad out of touch on at least one basic aspect learned years passed.

Parabola with equation y^2 = 2x, and parametric equation x = \frac{1}{2}t^2, y = t (t \in \Re) etc.

The problem is concered with finding the equation of the chord that joins the distinct points P and Q on the parabola w/ parameters t_1 and t_2 respectively, etc.

No that much of that was relevant to my quandray, which is in finding the gradient of PQ.
m = \frac{t_1 - t_2}{{\frac{1}{2}(t_1^2 - t_2^2)} = \frac{2}{t_1 + t_2} [\tex]<br /> edit: sorry, I guess I didn&#039;t get that tex tag right (what is wrong with it? Can I nest fractions like that?)<br /> <br /> m = (t1 - t2)/[.5(t1^2 - t2^2)] = 2/(t1 + t2).I can&#039;t remember (if I had learned it that is) how they arrived from the first to the latter fraction. <br /> <br /> An explanation would be quite welcome, thanks.
 
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Are you asking why:

\frac{t_1-t_2}{\frac{1}{2} ({t_1}^2-{t_2}^2)}=\frac{2}{t_1+t_2}

? If so, remember that a^2-b^2=(a-b)(a+b). And you can click on the equation above to see how I got it working. I think you have an extra {.
 
StatusX said:
Are you asking why:

\frac{t_1-t_2}{\frac{1}{2} ({t_1}^2-{t_2}^2)}=\frac{2}{t_1+t_2}

? If so, remember that a^2-b^2=(a-b)(a+b). And you can click on the equation above to see how I got it working. I think you have an extra {.


Thanks, I guess I wasn't looking at it the right way.

Did you need the {'s around each t in the denominator?
 
Yoss said:
Did you need the {'s around each t in the denominator?

No, but it makes it look nicer. {...}^2 puts the two above and to the right of the whole expression. If you just wrote t_1^2, you get some looks like a tensor element:

{t_1}^2 vs t_1^2
 
Yoss, your last equation... you used a backslash to close the tex tag is all you got wrong.
 
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