0
Okay, so you simply plug the equation of the line into the equation of the circle.
(The reason you do this is because whenever they intersect, their x and y values are equal)
I'll give an example.
Say, for instance, you want to know if y=x+1 (the line) intersects with x2+y2=4 (the circle)
Plug in the x+1 for the y in the circle.
So you now have:
x2+(x+1)2=4
(Make sure that you include the parenthesis!)
x2+(x+1)(x+1)=4
x2+x2+2x+1=4
2x2+2x+1=4
2x2+2x-3=0
Then you will use part of the quadratic formula, which is:
x=(-b±√(b2-4ac))/2a
For this problem, you're interested in what the value under the radical sign is.
(b2-4ac)
Plug in the numbers
22-(4)(2)(-3)
4-(-24)
4+24
28
When you plug in the numbers for b2-4ac (known as the discriminant)
If the final result is:
Greater than 0 - you have 2 intersection points
Equal to 0 - you have 1 intersection point
Less than 0 - they do not intersect
So, for your original question, if the discriminant ends up being equal to or greater than 0, then the line and the circle intersect.
I hope that made sense.
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The point at which a line and a circle intersect at exactly one point?
Tangent
Can a straight line intersect a circle at more than two points?
No.
What is radius equals 12 inches?
Every circle has a point called the centre. A straight line drawn through the centre and extending both ways to intersect with the circle at opposite points is called the diameter. A straight line drawn from the centre to intersect with one point of the circle is called the radius. In this case, the length of that straight line is 12 inches.
Line intersecting a circle in two points?
A line can be tangent to a circle in which case it intersects it in one point, it can intersect it in two points, or no points at all. So the choices are 0,1 or 2.
What coordinates do the international date line and arctic circle intersect?
It is 66°33′46.3″ North, 169 West.
The point where the tangent line intersects a circle?
A tangent line touches the circumference of a circle at just one point but it does not intersect the circle.
Was a secant line can intersect a circle in three points?
No it cannot.
The point at which a line and a circle intersect at exactly one point?
Tangent
Can a straight line intersect a circle at more than two points?
No.
Are line may intersect a circle at exactly one point?
A tangent line touches the circumference of a circle exactly at one point.
What is radius equals 12 inches?
Every circle has a point called the centre. A straight line drawn through the centre and extending both ways to intersect with the circle at opposite points is called the diameter. A straight line drawn from the centre to intersect with one point of the circle is called the radius. In this case, the length of that straight line is 12 inches.
Line intersecting a circle in two points?
A line can be tangent to a circle in which case it intersects it in one point, it can intersect it in two points, or no points at all. So the choices are 0,1 or 2.
What coordinates do the international date line and arctic circle intersect?
It is 66°33′46.3″ North, 169 West.
What is line intersect?
A line intersect is a point on a line where another line or object crosses the line.
Line xy and line wy intersect at?
They intersect at Y.
Do lines of latitude sometimes intersect explain?
Lines of latitude encircle the earth, with the Great Circle being the Equator. Each line of latitude is parallel to each other, so will never intersect.
Do two planes intersect at a point or a line?
Two planes intersect at a line
