SOLUTION: for what value(s) of k is the line 2x=3y+k a tangent to the parabola y=x^2-3x+4?

Question 156383: for what value(s) of k is the line 2x=3y+k a tangent to the parabola y=x^2-3x+4?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
for what value(s) of k is the line 2x=3y+k a tangent to the parabola y=x^2-3x+4?
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The slope of the tangent line is (2/3)
The slope of the parabola is 2x-3 for every value of "x".
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The tangent line will have the same slope as the parabola where
they touch.
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2x-3 = 2/3
2x = 11/3
x = 11/6 is the point where they touch.
The corresponding y-value is (11/6)^2-3(11/6)+4 = (121/36)-(11/2)+4 = 67/36
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Find the value of "k"
2(11/6) = 3(67/36) + k
(11/3) = (67/12) = k
k = -1.9167..
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Cheers,
Stan H.

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