SOLUTION: The line y = mx+3 and the curve x^2+c intersect only at one point. Where " c" and "m" are constants. A. Find the possible set of values for "c" & " m" B. find the coordinates

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Question 881469: The line y = mx+3 and the curve x^2+c intersect only at one point. Where " c" and "m" are constants.
A. Find the possible set of values for "c" & " m"
B. find the coordinates of the point of intersection using the values obtained in A.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
y=mx%2B3
y=x%5E2%2Bc
Set them equal to each other.
mx%2B3=x%5E2%2Bc
x%5E2-mx%2Bc-3=0
Since they only intersect at one point, the discriminant equals zero.
m%5E2-4%28c-3%29=0
m%5E2=4%28c-3%29
If order for m to be real, c-3%3E=0, or c%3E=3
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.
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When c=3,m=0
Then the line becomes, y=3 and the parabola becomes, y=x%5E2%2B3
y=3
x%5E2%2B3=3
x=0
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.
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When c=4,m=2
Then the line becomes, y=x%2B3 and the parabola becomes, y=x%5E2%2B4
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2x%2B3=x%5E2%2B4
x%5E2-2x%2B1=0
%28x-1%29%5E2=0
x=1
y=2%281%29%2B3=5