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innocentman69
02.09.2020 •
Mathematics
Consider the Line L(t) = <2+t,5-4t>. Then L intersects:
The x- axis at the point (3.25,0) when t = 5/4
The y- axis at the point (0, 13) when t = -2
The parabola y = x^2 at the points ___ and ___ when t = and
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Ответ:
The parabola
at the points
and
when
and ![t=t_{2}=-4-\sqrt{17}](/tpl/images/0737/6568/9c59e.png)
Step-by-step explanation:
We have the following line written in parametric form :
In order to find the intersection between
and the parabola
we know that ''
'' is the x-coordinate of the line and ''
'' is the y-coordinate of the line. Now, to solve this problem we need to find the values of ''
'' in which the intersection occurs. We can do this by replacing the components ''
'' and ''
'' of
in the equation of the parabola ⇒
In the parabola :
⇒ ![5-4t=(2+t)^{2}](/tpl/images/0737/6568/e074a.png)
Solving the equation we find that :
Using the quadratic formula with
We find that the two possible values for t :
are
and ![t_{2}=-4-\sqrt{17}](/tpl/images/0737/6568/b9f75.png)
This values
and
are the values of the parameter t where the line intersects the parabola so we can find the points by replacing the values of the parameter in the equation
:
The final answer is
The parabola
at the points
and
when
and ![t=t_{2}=-4-\sqrt{17}](/tpl/images/0737/6568/9c59e.png)
Ответ: