Write a formula for the distance between a point x y on the

Write a formula for the distance between a point (x, y) on the graph of y = x6 and the point (3, 6). Express your answer in terms of x.

Solution

The distance d between two points (x1, y1) and (x2, y2) is
d = [(x2 – x1)^2 + (y2 – y1)^2]

Let (x,y) be a point on the graph of the function y = x⁶.
Use the distance formula to write an expression for the distance d between (x,y) and (3,6). [To do this I will replace x2 and y2 with x and y, and I’ll replace x1 and y1 with 3 and 6]

d = [(x2 – x1)^2 + (y2 – y1)^2]
d = [(x – 3)^2 + (y – 6)^2]
d = [(x – 3)^2 + (y -6)^2]
Now replace y with x^6
d = [(x – 3)^2 + (x^6 -6 )^2]