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postillan4

Answered question

2021-05-13

The point (x,y) lies on the graph of $y = x ³$ . Write the distance d between (1, 0) and (x,y) in terms of x. Write the distance d between (0, 1) and (x,y) in terms of x.

Answer & Explanation

komunidadO

Skilled2021-05-14Added 86 answers

Use the Distance Formula:

d = \sqrt{{(x 2 - x 1)}^{2} + {(y 2 - y 1)}^{2}}

The distance between (1,0) and (x,y) is:

d 1 = \sqrt{{(x - 1)}^{2} + {(y - 0)}^{2}}

d 1 = \sqrt{{(x - 1)}^{2} + y^{2}}

Since

y = x^{3}

, we substitute:

d 1 = \sqrt{(x^{2} - 2 x + 1) + {(x^{3})}^{2}}

d 1 = \sqrt{(x^{2} - 2 x + 1) + x^{6}}

d 1 = \sqrt{(x^{6}) + x^{2} - 2 x + 1}

Similarly, the distance between (0,1) and (x,y) is:

d 2 = \sqrt{{(x - 0)}^{2} + {(y - 1)}^{2}}

d 2 = \sqrt{(x^{2}) + {(y - 1)}^{2}}

Since

y = x^{3}

, we substitute:

d 2 = \sqrt{(x^{2} + {(x^{3} - 1)}^{2})}

d 2 = \sqrt{x^{2} + (x^{6} - 2 x^{3} + 1)}

d 2 = \sqrt{x^{6} - 2 x^{3} + x^{2} + 1}

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