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The line y= 3x-p+1 is a tangent to the parabola y= x2

Evaluate p 

 

Thank you 

 Oct 24, 2017
 #1
avatar+27558 
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"The line y= 3x-p+1 is a tangent to the parabola y= x2

Evaluate p "

 

.

 Oct 24, 2017
 #2
avatar+98196 
+2

The slope at any point on the parabola = 2x

 

The slope of the line is 3

 

So.....equating slopes, we have that     2x = 3 ⇒   x  =  3/2

 

So....at x = 3/2,  x^2  =  9/4  = y

 

So.......to find p we have

 

9/4  =  3(3/2) - p + 1

 

9/4  =  9/2 + 1 - p

 

9/4  = 22/4 - p

 

p = 13/ 4

 

Here's the graph : https://www.desmos.com/calculator/kzzakejx7h

 

cool cool cool

 Oct 24, 2017
edited by CPhill  Oct 24, 2017

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