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

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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.

• x² + y² = 100

center (0, 0)

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.

• 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)

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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