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# At what points does the line y

Let L whose be a straight line in the xy-plane whose equation is of the form
y - 8 = m(x - 2).

(a) Determine all the points in the xy-plane where the line L intersects the curve y = 2x^2 .

(b) Using the results of Part (a), determine whether there are any values of m such that L intersects the curve y = 2x^2 in exactly one point.

#### Solution Preview

Line Intersection Problem
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Let L whose be a straight line in the xy-plane whose equation is of the form
y - 8 = m(x - 2).

(a) Determine all the points in the xy-plane where the line L intersects the curve y = 2x^2

The line y - 8 = m(x - 2) can be rewritten as y = mx - 2m + 8.

Set the y's from the line and the curve equal to each other and solve for x:

mx - 2m + 8 = 2x2

0 = 2x2 - mx + (2m - 8)

x = m ± ...

#### Solution Summary

This solution provides step by step calculations and answers for the line intersection problem in an attached Word document.

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