2 Let pxy be a point on the graph of yx3 Express the distanc

2. Let p=(x,y) be a point on the graph of y=x^3. Express the distance d from P to the point (2, 0) as function of x. What is d if x=-1?

Y = x^3

Point ( 2, 0)

Distnace between any point on Y = x^3 be (x, y)

So, distnace between (x, y) and ( 2, 0) is given as:

d = sqrt( (x-2)^2 +( y-0)^3 )

= sqrt( ( x-2)^2 +y^2 )

Now we know y = x^3 ----> y^3 = x^6

So, d = sqrt( (x-2)^3 +x^6)

So we have distance in terms of x :

d = sqrt( (x-2)^3 +x^6)

if d=1

So, 1 = d = sqrt( (x-2)^3 +x^6)

if x=-1 ; d= sqrt( (-1-2)^2 +1) = sqrt( 10)