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Equations of straight lines

1. Find the equation of straight lines satisfying the following conditions:

The product of x-intercept and the y-intercept is 20, and parallel to the line

5x+2y-6=0

2. Find the equation of line(s) such that perpendicular to L1: x-y=0, and the

area of the triangle enclosed by the line and the axes is 7/1/5 .

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  • 土扁
    Lv 7
    10 年前
    最愛解答

    1. Find the equation of straight lines satisfying the following conditions: The product of x-intercept and the y-intercept is 20, and parallel to the line 5x+2y-6=0

    Since the required line is parallel to the line 5x + 2y - 6 = 0

    Let 5x + 2y + c = 0 be the required line.

    When x = 0, y = -c/2

    Hence, y-intercept of the required line = -c/2

    When y = 0, x = -c/5

    Hence, x-intercept of the required line = -c/5

    The product of the x-intercept and the y-intercept:

    (-c/2)(-c/5) = 20

    c² = 200

    c = 10√2 or c = -10√2

    The required line is:

    5x + 2y + 10√2 = 0 or 5x + 2y - 10√2 = 0

    =====

    2. Find the equation of line(s) such that perpendicular to L1: x - y = 0, and the area of the triangle enclosed by the line and the axes is 7/1/5 .

    Slope of L1 = -1/(-1) = 1

    Slope of the required line = -1/1 = -1

    Let x + y + c = 0 be the required line.

    When x = 0, y = -c

    y-intercept = -c

    When y = 0, x = -c

    x-intercept = -c

    Area of the triangle enclosed by the line and the axes:

    c²/2 = (7 and 1/5)

    c²/2 = 36/5

    c² = 360/25

    c = (6/5)√10

    The required line is:

    x + y + (6/5)√10 = 0 or x + y + (6/5)√10 = 0

    資料來源: 土扁
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