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What is the value of k so that y = x^2 + 3k + 4 and x + y + 3 = 0 meet at only one point?
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There is an error in your question, the equation of the curve should be given as y = x^2 + 3k + 4
We have to determine the value of k which ensures that the curve y = x^2 + 3k + 4 and the line x + y + 3 = 0 meet at only one point.
x + y + 3 = 0
=> y = -x - 3
substitute in y = x^2 + 3k + 4
=> -x - 3 = x^2 + 3k + 4
=> x^2 + x + 3k + 7 = 0
This equation should have only one solution. That is possible if
(1)^2 - 4*1*(3k + 7) = 0
=> 1 - 12k - 28 = 0
=> 12k = -27
=> k = -27/12
The required value of k is -27/12
Posted by justaguide on August 8, 2011 at 12:11 AM (Answer #1)
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