Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

Trending News

Promoted
Guillermo
Lv 7
Guillermo asked in Science & MathematicsGeography · 8 years ago

Please, friends, Help! A point P moves so that the sum of the squares of the distances to the lines 3 * x-y +4?

= 0 and x +3 * and 7 = 0 is always equal to 2. Find, identify and trace the locus of P.

Thanks!

Update:

x +3 *y and 7 = 0

2 Answers

Relevance
  • bpiguy
    Lv 7
    8 years ago
    Favorite Answer

    Looks like your two lines might be 3x - y + 4 = 0 and x + 3y + 7 = 0. These can be rewritten as

    y = 3x + 4 and y = -1/3 (x + 7)

    These two lines are perpendicular because the product of their slopes is -1. The lines intersect at

    3x + 4 = -1/3 (x + 7) ==> 9x + 12 = -x - 7 ==> 10x = -19 ==> x = -1.9

    y = 3 • 1.9 + 4 = 9.7

    So your answer is a circle centered at (-1.9, 9.7) with radius √2. The locus of P is

    (x + 1.9)^2 + (y - 9.7)^2 = 2 (Answer)

  • longknowledge
    Lv 7
    8 years ago

    You might want to ask this question also under the categories Homework Help or Mathematics.

Still have questions? Get your answers by asking now.