try to find an equation using distance formula.

Question

Write a formula for the distance between a point (x, y) on the graph of y = x^4 and the point (5, 5). Express your answer in terms of x.

so I attempted this a couple times and I came up with

((5-x^2)+(5-x^4))^1/2

and

sqrt(x^8+x^2-10x)

These are both wrong and I was wondering if you could show me the right answer and how you got it. I'm so confused on how to manipulate the distance formula. Thank you.

Answer 1

Since y = x⁴, an (x,y) point on the curve is (x,x⁴).  You want the distance between (x, x⁴) and (5,5).

 

d = √[(x-5)² + (x⁴-5)²]