Let P=(x,y) be a point on the graph of y=(x^2)-25

Question

Express the distance D from P to the point (1,0) as a function of x.

What is D if x=2?

Answer 1

y = x² - 25

 

The coordinates of any point on the graph are P = (x,x²-25).  The distance D from any point P to the point (1,0) can be computed using the Pythagorean Theorem.

 

D = [(x-1)² + (x²-25)²]^1/2

 

Click here to see an illustration:

 

http://www.wyzant.com/resources/files/297341/distance_between_point_and_graph

 

For x = 2:

 

D = [(2-1)² + (2²-25)²]^1/2

 

   = [1 + (-21)2]1/2

 

   = (442)^1/2

 

   ≅ 21.02

Answer 2

Your fixed point is (1,0).  Your variable point is (x,y) = (x,x²-25).

 

 

The distance between them uses the distance formula: D = √[(x₂ - x₁)² + (y₂ - y₁)²]

 

 

In this case, D = √[(x - 1)² + (x² - 25 - 0)²] = √[(x - 1)² + (x² - 25)²]

 

 

For x = 2, D = √[(2 - 1)² + (2² - 25)²] = √[1 + (-21)²] = 21.02