Problem with a syllabus of math. about equations of a circle and a line

[jean05]

Hi
i have a important test in a few months, and i have a problem with this point in the syllabus.




that point say about relative positions of a circle and a line but i search in google and i dont find something that fit in well,with what say in the syllabus. My question is, if someone can tell me what is about or where i can learn it?
i really appreciate that, thanks (sorry about how i wrote this, im not very good writting in english)

 

[mmm4444bot]

Hi
i have a important test in a few months, and i have a problem with this point in the syllabus.

View attachment 7634


that point say about relative positions of a circle and a line but i search in google and i dont find something that fit in well,with what say in the syllabus. My question is, if someone can tell me what is about or where i can learn it?
i really appreciate that, thanks (sorry about how i wrote this, im not very good writting in english)

Hello. Relative positions of two objects means how the objects appear together. Is one above the other, or below? Is one to the left of the other, or to the right? Do they intersect, or not?

For example, they could give you two equations (the first for a circle and the second for a line). If these objects are graphed together in the xy-coordinate system, what are their positions relative to each other?

(x-4)^2 + (y-1)^2 = 10

3x - y = -4

The graph is attached. This situation could model the paths of an orbiting planet and a killer asteroid. In order to know whether the asteroid might strike the orbiting planet, we need to consider the relative positions of their paths. This can be done by looking at a graph OR algebraically by solving equations together to check for intersection points.

Cheers :cool:

 

[jean05]

Hello. Relative positions of two objects means how the objects appear together. Is one above the other, or below? Is one to the left of the other, or to the right? Do they intersect, or not?

For example, they could give you two equations (the first for a circle and the second for a line). If these objects are graphed together in the xy-coordinate system, what are their positions relative to each other?

(x-4)^2 + (y-1)^2 = 10

3x - y = -4

The graph is attached. This situation could model the paths of an orbiting planet and a killer asteroid. In order to know whether the asteroid might strike the orbiting planet, we need to consider the relative positions of their paths. This can be done by looking at a graph OR algebraically by solving equations together to check for intersection points.

Cheers :cool:

Ahhh, Thanks
so the answer is that,the line dont intercept the circle?
if in some problem the line intercept the circle, we need to include the points in which the line intercept the circle?

 

[mmm4444bot]

Ahhh, Thanks
so the answer is that,the line dont intercept the circle?

If the questions is "Does the line intersect with the circle?", then, yes, your answer could be "The line does not intersect with the circle."

if in some problem the line intercept the circle, we need to include the points in which the line intercept the circle?

It depends on the problem statement. If the instructions ask you for the coordinates of any intersection points, then, yes, you need to state them.

There are other questions about relative positions which do not involve intersections. For example, a different problem statement might tell you right away that a line does not intersect a circle. Like this one:

A horizontal line is positioned some distance above a circle. What is the distance between the line and the circle?

y = 5

x^2 + y^2 = 4

The blue sentence gives us an idea of how the line and circle are positioned relative to each other; they don't intersect. Your job will be to determine the coordinates of the two closest points, from the information that they will teach you about interpreting the different parts of each equation. Once you have the coordinates, you will use the Distance Formula, to calculate the distance between them.

In this exercise, the closest points are (0,2) on the circle and (0,5) on the line. Therefore, the horizontal line is positioned 3 units above the circle.

 

[jean05]

If the questions is "Does the line intersect with the circle?", then, yes, your answer could be "The line does not intersect with the circle."




It depends on the problem statement. If the instructions ask you for the coordinates of any intersection points, then, yes, you need to state them.

There are other questions about relative positions which do not involve intersections. For example, a different problem statement might tell you right away that a line does not intersect a circle. Like this one:

A horizontal line is positioned some distance above a circle. What is the distance between the line and the circle?

y = 5

x^2 + y^2 = 4

The blue sentence gives us an idea of how the line and circle are positioned relative to each other; they don't intersect. Your job will be to determine the coordinates of the two closest points, from the information that they will teach you about interpreting the different parts of each equation. Once you have the coordinates, you will use the Distance Formula, to calculate the distance between them.

In this exercise, the closest points are (0,2) on the circle and (0,5) on the line. Therefore, the horizontal line is positioned 3 units above the circle.

Ah, ok perfect. Thanks