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What are three ways of proving that the line of y equals 2x plus 5 over 4 is a tangent to the curve of y squared equals 10x showing work?
Wiki User
∙ 8y ago
If: y = 2x+1.25 and y^2 = 10x
Then: (2x+1.25)^2 = 10x
So: 4x^2 +5x+1.5625 = 10x => 4x^2 -5x+1.5625 = 0
Proof 1: The discriminant of the quadratic equation = 0
Proof 2: The solutions of the quadratic both equal 5/8
Proof 3: Plot the line of y = 2x+5/4 and the curve of y^2 = 10x on the Cartesian plane which will result in a contact point of (5/8, 5/2) making the line tangent to the curve.
Wiki User
∙ 8y ago
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-2
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