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Consider the parabola: x=2(y-2)^2 + 3, and the point P (3,4) (a)  Write a polynomial expres sion for the distance d from point P to an arbitrary point Q on the parabola. (b)  Make a plot of d versus y for . (c)  Determine the coordinates of Q if d = 3 (there are two points). (d)  Determine the coordinates of Q that correspond to the smallest d, and calculate the corresponding value of d. (e)  Make a plot that shows the parabola, point P, the two points from part (c), and the point from part (d).

Consider the parabola: x=2(y-2)^2 + 3, and the point P (3,4) (a)  Write a polynomial expres sion for the distance d from point P to an arbitrary point Q on the parabola. (b)  Make a plot of d versus y for . (c)  Determine the coordinates of Q if d = 3 (there are two points). (d)  Determine the coordinates of Q that correspond to the smallest d, and calculate the corresponding value of d. (e)  Make a plot that shows the parabola, point P, the two points from part (c), and the point from part (d).

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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  1. Consider the parabola: x=2(y-2)^2 + 3, and the point P (3,4)

    1. (a)  Write a polynomial expres

      sion for the distance d from point P to an arbitrary point Q on the parabola.

    2. (b)  Make a plot of d versus y for .

    3. (c)  Determine the coordinates of Q if d = 3 (there are two points).

    4. (d)  Determine the coordinates of Q that correspond to the smallest d, and

      calculate the corresponding value of d.

    5. (e)  Make a plot that shows the parabola, point P, the two points from part

      (c), and the point from part (d).

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