Math math math?

Question

let P(x,y) be a point on the graph of y=4x. Express the distance d from P to the point (-1,0) as a function of x

options 

a) d=√17xˆ2 +2x+1 .

b) d=√17xˆ2 +1 

c) d=√17xˆ2 +4x+1 

d) d=√17xˆ2 +8x+1 

e) d=√17xˆ2 -8x+1 

f) d=√17xˆ2 -2x+1

Answer 1

The points are P(x, y) and (-1, 0).

Substitute (x₁, y₁) = (x, y) and (x₂, y₂) = (-1, 0) in the distance fromula: d = √[(x₂ - x₁)² + (y₂ - y₁)²].

d = √[(-1 - x)² + (0 - y)²]

d = √[1 + 2x + x² + y²]

The point P(x, y) lie on the line y = 4x.

d = √[1 + 2x + x² + (4x)²]

d = √(1 + 2x + 17x²)

d = √(17x² + 2x + 1).

The option a is correct.