The value of
such that the line
is tangent to the parabola
is
.
If
is a line <em>tangent</em> to the parabola
, then we must observe the following condition, that is, the slope of the line is equal to the <em>first</em> derivative of the parabola:
(1)
Then, we have the following system of equations:
(1)
(2)
(3)
Whose solution is shown below:
By (3):

(3) in (2):
(4)
(4) in (1):



The value of
such that the line
is tangent to the parabola
is
.
We kindly invite to check this question on tangent lines: brainly.com/question/13424370
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Answer:
Slope = 0
So, the line is parallel to x-axis
Step-by-step explanation:
(x₁ , y₁) = (-8, -8) & (x₂ ,y₂) = (6 , -8)
![Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\\=\frac{-8-[-8]}{6-[-8]}\\\\=\frac{-8+8}{6+8}\\\\= 0](https://tex.z-dn.net/?f=Slope%20%3D%20%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D%5C%5C%5C%5C%5C%3D%5Cfrac%7B-8-%5B-8%5D%7D%7B6-%5B-8%5D%7D%5C%5C%5C%5C%3D%5Cfrac%7B-8%2B8%7D%7B6%2B8%7D%5C%5C%5C%5C%3D%200)