Circle graph, y^2+x^2=100, and a linear function g(x). Will they intersect?

NetherCraft 0

The X is -1,0, and 1

The g(x) is -22,-20, and -18

I’m trying to study and i just cant figure this one out. Thanks to anyone who is willing to help.

5 Answers

  • x² + y² = 100

    center (0, 0)

    radius = 10

    From the (x, g(x)) data, the slope of g(x) is 2 and the y-intercept is -20.

    g(x) = 2x – 20

    perpendicular from center of circle to g(x):

    y = (-½)x

    point of intersection: (8, -4)

    distance between center of circle and (8, -4) = √(8² + 4²) = √82 < 10, so point of intersection is inside the circle. circle and g(x) intersect, although not at (8, -4). But they didn’t ask where.

    http://www.flickr.com/photos/dwread/11950358784/

  • If the line passes through (-1, -22), (0, -20), and (1, -18)

    Then the y-intercept is b = -20.

    The slope is m = (-18 – (-20)) / (1 – 0) = 2

    So g(x) = mx + b = 2x – 20

    CHECK:

    g(-1) = 2(-1) – 20 = -22

    g(0) = 2(0) – 20 = -20

    g(1) = 2(1) – 20 = -18

    So we need to solve

    y = 2x – 20 and x^2 + y^2 = 100

    x^2 + (2x – 20)^2 = 100

    x^2 + 4x^2 -80x + 400 = 100

    5x^2 – 80x + 300 = 0

    5(x^2 – 16x + 60) = 0

    (x – 6)(x – 10) = 0

    x = 6 or x = 10

    If x = 6, y = 2(6) – 20 = -8

    If x = 10, y = 2(10) – 20 = 0

    So the two curves intersect at the points

    (6, -8) and (10, 0)

  • g(x): (-1,-22),(0,-20),(1,-18)

    => g(x) = y = 2x – 20

    Plug into equation of circle:

    (2x – 20)^2 + x^2 = 100

    4x^2 – 80x + 400 + x^2 – 100 = 0

    5x^2 – 80x + 300 = 0

    x^2 – 16x + 60 = 0

    (x – 10)(x – 6) = 0

    x = 10 or x = 6

    => y = 0 or y = -8

    So, they intersect in points (10,0) and (6,-8)

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    RE:

    Circle graph, y^2+x^2=100, and a linear function g(x). Will they intersect?

    The X is -1,0, and 1

    The g(x) is -22,-20, and -18

    I’m trying to study and i just cant figure this one out. Thanks to anyone who is willing to help.

  • Your g(x) is -22, -20, -18 does not make sense.

    There should be some form of linear eq’n, such as g(x) = mx + c

    y^2 + x^2 = 10^2

    This is a circle centred on (0,0) The origin, with a radius of ’10’.

    On the coordinate axes the four intersections, with the circle and the coordinate axes, are ; – (10,0) , (0,10) , (-10, 0) & (0, -10).

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