Function of first components, Disc

[danode]

Hi!
I got a problem I am struggeling to solve:

I got a disc with radius p<1/2, and it is rolling on the parabola y=x^2. The center of the disc have the coordinates (X,Y).

s(x)= (x, x^2)

b) Find X and Y as functions of the first component in s(x).



Greetings from Norway!

 

[mmm4444bot]

Hi!
I got a problem I am struggeling to solve:

I got a disc with radius p<1/2, and it is rolling on the parabola y=x^2. The center of the disc have the coordinates (X,Y).

s(x)= (x, x^2)

b) Find X and Y as functions of the first component in s(x).

View attachment 7725

Greetings from Norway!

Hi. What have you tried or thought about so far?

Do you realize that line segment p will always be perpendicular to the line which is tangent to the parabola at the intersection point?

What do you remember about the relationship between slopes of perpendicular lines?