In Exercises 45–52, use your answers from Exercises 41–44 and ...

Question

In Exercises 45–52, use your answers from Exercises 41–44 and the parametric equations given in Exercises 41–44 to find a set of parametric equations for the conic section or the line.

Line: Passes through (−2,4) and (1,7)

Accepted Answer

Welcome back everyone. We want to determine the parametric equations for the line segment connecting the points negative 35 and four negative two. A says they are X equals T minus three and Y equals T plus five BX equals seven T minus three and Y equals negative 70 plus five CX equals T plus four and Y equals negative T minus two and DX equals T and Y equals negative T. Now to figure out these parametric equations, let's first try to understand what we're working with here. Let's try to learn a little bit more about our line segment by drawing a sketch of that segment on our graph. Now we know it connects the points negative 35 where that would be in the second quadrant. OK. And four negative two. So that would be in the fourth quadrant. So now here this is our line segment. Now, if we think about it, if we have our direction vector, then we should be able to use it in our parametric equation for both our X and Y equations. So let's say that our direction vector here starting at the initial point of negative 35. OK. Is V. Now we know then that V is going to be equal to the difference between the coordinates of our points. So that's gonna be four minus negative three. OK. And negative two minus five which is going to be equal to seven, negative seven. This is our direction vector, right? So let me, let me actually write that here where V is the direction vector know that we have a direction vector using the points negative 35 as our initial point. This means then that the parametric equation for X is going to be equal to negative three or starting point plus 70. OK. The value in our direction vector is going seven units to the right and Y is going to be equal to. But let me write it beside it here Y is gonna be equal to negative 70 or sorry five. OK? Five. Our initial point minus seven. Now, if we rearrange to have our variable first, then X is equal to seven minus three and Y equals negative seven plus five, these are the parametric equations for our line segment. Therefore, B is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

In Exercises 45–52, use your answers from Exercises 41–44 and the parametric equations given in Exercises 41–44 to find a set of parametric equations for the conic section or the line.

Line: Passes through (−2,4) and (1,7)

Key Concepts

Parametric Equations of a Line

Vector Representation of a Line

Using Given Points to Determine Parameters

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