quazzimotto said:
I get answer of y = 1-(1/4)x as detailed in link.
Your image is a 2.7 meg graphic that measures 5102 by 6599 pixels and displays almost entirely textual material.
In the future, it might be helpful if you posted content that most of us could reasonably view. I have surfed, attempted to view, downloaded, and re-opened the graphic, in order to see what you did. Most won't bother.
Thank you for your consideration.
Eliz.
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P.S. to other viewers: This is what was in the graphic:
x<sup>2</sup> + y<sup>2</sup> = r<sup>2</sup>
. . .\(\displaystyle y\,=\,\pm\,\sqrt{r^2\,-\,y^2}\)
6) Find the equation of the tangent line to the curve at the point t = 1. [student note: (2, 1)] The curve is defined by the following set of parametric equations:
. . . . .x = 3t<sup>2</sup> - 2t - 1
. . . . .y = 1 / t
. . . . .t
. . . . .x
. . . . .y
. . . . .-------------------------
. . . . .0
. . . . .1
. . . . .undef
. . . . .1
. . . . .2
. . . . .1
[student note: graph looks like positive half of y = 1/x, with directional arrows leading down and then to the right]
1) Find derivative to get slope of tangent line
. . . . .\(\displaystyle \L \frac{dy}{dx}=\frac{\left(\frac{dy}{dt}\right)}{\left(\frac{dx}{dt}\right)}=\frac{(-1)t^{-1-1}}{6t-2}=\frac{\left(\frac{-1}{t^2}\right)}{\left(\frac{6t-2}{1}\right)}=\frac{-1}{t^2(6t-2)}=\frac{-1}{2t(3t-1)}\)
When t = 1, then m = -1/4.
2) Derivative in terms of t which is slope needs to be converted to x,y coordinate pair.
When t = 1, x = 2, y = 1.
. . . . .x
. . . . . . . .|
. . . . .y
---------------------|------------------
2 = 3t<sup>2</sup> - 2t + 1
. .|
. . . . .1 = 1/t
1 = t(3t - 2)
. . . ..|
solve ()
. . . . . . . .|
t = -1/3 or
t = 1.|
. . . . .t = 1
Any t which appears in both lists will give point.
. . . . .\(\displaystyle \L \frac{dy}{dx}=\frac{-1}{2t^2(3t-1)}=\frac{-1}{2(1)^2(3t-1)}=\frac{-1}{4}\)
Tangent line is given by Y = F(x), where x = a
Then Y = F(a) + (dy/dx)(x - a), F(a) = x = 2
Since, at t = 1, x = 2, y = 1, and since m = dy/dx, then
Tangent Line Equation --> Y = 1 - (1/4)x
