The line y= 3x-p+1 is a tangent to the parabola y= x^{2}

Evaluate p

Thank you

Ashreeta
Oct 24, 2017

#2**+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

CPhill
Oct 24, 2017