Finding intersection lines and circles graphically

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How to find the intersection of circles and lines.

Three possibilities of Circles and Lines

0 points of intersection
1 point of intersection
2 points of intersection

You can find these points graphically and the video works some examples.

Transcript

Intersection of Circles and Lines and we are covering this for our summer geometry course. Over here on the left we have a picture and it is very visual and how many point of intersection does it have? It has zero because they don't touch at all. A circle and a line may never touch, but a circle and a line can touch in one place and we call this a point of tangency. You guys have learned that when you did your circle units. A circle and a line can have two points of intersection when you have a secant go through the circle. So we have three choices. either they don't touch, they touch once, or they touch twice. What does it look like to graph these and what are the points of intersection. We need to know how to graph a circle, which we have learned, and need to know how to graph an equation of a line. You probably learned this in 7th grade. Here we go let's try to do. For a circle nothing is added to x and y and (0,0) is the center. The radius will be the square root of 4 or just 2. So we will plot our center and count up to the right 2,down,and to the left, and draw in our circle. So there is our circle. Now let's draw our line, and in order to graph a line we need to solve for y and we get -y = -2x +5 Divide by negative and we get y=2x-5. So we go down to 5 and plot up 2 over 1,and repeat, and what do you see? How many points of intersection do you have? It looks like none. This circle and line combination has no points of intersection, and that may happen. This next one is missing some parenthesis so if would like add them in. We have (x-3)^2 + (y-2)^2 =9 Our center is (3-2) Remember to take the opposite signs. Radius =3 (Square root of 9) Go up 3,right three,down three, and left 3, and plot our circle. It may not be perfect, if you have a compass you can make a better circle. Then y=5. What kind of a line is y=5. This is a horizontal line and it crosses at -5 and will go across here. So how many points of intersection do the circle and line have? Yes 1 and it is at the point +3,-5,and that is the solution.

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