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How do you prove that the line y equals 2x plus 5 over 4 touches the curve y squared equals 10x?
Wiki User
∙ 13y ago
Y2=10X and Y=2x+5 will never touch each other. If there is a touch point then there will be a common value (Touch point) of x and y which will satisfy both equations. But there is no common point so it is not possible
Improved Answer:
equation 1: y = 2x++5/4 => y2 = 4x2+5x+1.5625 when both sides are squared
equation 2: y2 = 10x
By definition: 4x2+5x+1.5625 = 10x => 4x2-5x+1.5625 = 0
If the discriminant b2-4ac is equal to zero then the line is tangent to the curve:
b2-4ac = (-5)2-4*4*1.5625 = 0
Therefore the discriminant is zero thus proving that the line is tangent to the curve.
Wiki User
∙ 13y ago
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