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Graph the circle and the line in order to find the points of intersection.
Graph:
Point of intersection: (-4,4)
By graphing the given equations, we can determine the number of points of intersection between the circle and the line. To do so, we need to graph both figures. Let's consider one of them at a time.
(x+1)^2+(y-1)^2=18 ⇕ (x-( -1))^2+(y- 1)^2=( sqrt(18))^2 The center of the circle is the point ( -1, 1), and its radius is sqrt(18). We can graph the circle using this information.
To graph the line, we will need its equation to be in slope-intercept form to help us identify the slope m and y-intercept b. Let's rewrite the equation in slope-intercept form, highlighting the m and b value.
Given Equation | Slope-Intercept Form | Slope m | y-intercept b |
---|---|---|---|
y=x+8 | y= 1x+ 8 | 1 | (0, 8) |
To graph this equation, we will start by plotting its y-intercept. Then, we will use the slope to determine another point that satisfies the equation, and connect the points with a line.
We can see that the circle and the line intersect at exactly two points. Let's identify them.
The point of intersection is (-4,4).