Intersection of circlesssss!

So today we will be learning about how to find the intersection of a line and a circle when given a line and cirlce.

1. the first thing your going to do is take the line equation and solve for y.

2. take the line equation, solved for y, and plug it into the cirlce equation for y.

3. The next step is to combine all the terms and distibute the powers and then use foil to help expand .

4.Then you solve the quadratic and will get 2 x's. X will equal one number, and then X will equal another number.

5. Next you will take one of those numbers and plug it into the line equation as an x and solve and that will be one y. Take the other number and do the same and that will be your second y.

6. you will have 2 points and that will be where the line intersects the circle. If you get an i then that mean it doesnt not intersect.


Ex: x+y=23, x^2+y^2=289

1.y=x-23

2. x^2+(x-23)^2=289

3. x^2+x^2-46x+240

4. x=8 x=15

5. 23-8=y y=15 23-15=y y=8

6. (8,15) (15,8)

The line will intersect the circle at (8,15) and at (15,8).