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penguin_alexa
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How do I algebraically prove how many times the line y=-5 intersects the circle (x-3)^2 + (y+2)^2 =25?
The formula for finding the points of intersection between a line and a circle is to substitute the equation of the line into the equation of the circle. This will result in a quadratic equation, which can be solved using the quadratic formula.
A line and a circle can have either 0, 1, or 2 points of intersection. If the line is tangent to the circle, there will be 1 point of intersection. If the line is a secant, there will be 2 points of intersection. If the line does not intersect the circle at all, there will be 0 points of intersection.
No, a line and a circle can only have a maximum of 2 points of intersection. This is because a circle is a two-dimensional shape and a line is a one-dimensional shape, so they can only intersect at a maximum of 2 points.
You can determine the points of intersection between a line and a circle by graphing the equations and looking for where they intersect. The coordinates of the intersection points will be the points of intersection between the line and the circle.
Yes, there are a few special cases to consider when finding the points of intersection between a line and a circle. If the line is parallel to the circle, there will be no points of intersection. If the line is coincident with the circle, there will be an infinite number of points of intersection. Additionally, if the line and the circle have the same center, there will be an infinite number of points of intersection.