How do i get the point of intersection of a line and a circle?

Just make sure to properly substitute the values and solve for the variables. This method should give you the point of intersection between the line and the circle.In summary, to find the point of intersection between a line and a circle, you need to isolate one variable in one equation, substitute it in the other equation, and solve for the remaining variable. This method should give you the desired solution.
  • #1
rakeshthp
6
0
How do i get the point of intersection of a line and a circle.. I got lots of information on this topic, but my requirement is not matching..

I got a line whose one end point lies at the origin of the circle.. and other end lies somewhere outside the circle.. Now i need the point of intersection of this line and circle..

Any way to get the solution for this problem..??

Thanks in advance
 
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  • #2
Hi there,

To get the intersection, you simply need to isolate one variable (let's say y) in one equation, and substitute it in the other. Then you have an equation with only one variable, which should be simple to solve. Once you have solve the equation, replace the solution in one of the first euqation to find the value of the second variable.

Cheers
 
  • #3
You mean to say that, if,
y = mx + b; and

x^2 + y^2 = r^2

are two equations, then subst y=mx+b in eqt of circle..??then solve this equation and then get value for x.. den subst x in y=mx+b and get value of y..

am i right..?
 
  • #4
As simple as that.
 

1. What is the formula for finding the point of intersection of a line and a circle?

The formula for finding the point of intersection of a line and a circle is to first solve for the x and y coordinates of the point of intersection using the equations of the line and circle. These coordinates can then be plugged into the point-slope formula to find the equation of the line passing through the point of intersection.

2. How do I find the equations of the line and circle to use in the formula?

To find the equation of the line, you will need two points on the line. Use the slope formula to find the slope of the line, and then plug one of the points and the slope into the point-slope formula to find the equation of the line. To find the equation of the circle, you will need the center coordinates and the radius. Use the formula (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center and r is the radius, to find the equation of the circle.

3. Can I use any method to solve for the point of intersection?

Yes, there are multiple methods for finding the point of intersection of a line and a circle. One method is to set the equations of the line and circle equal to each other, and then solve for the x and y coordinates. Another method is to use the substitution method, where you substitute one equation into the other and solve for one variable, then use that value to solve for the other variable.

4. Are there any special cases I need to consider when finding the point of intersection?

Yes, there are a few special cases to consider. If the line is tangent to the circle, there will only be one point of intersection. If the line is a secant line, there will be two points of intersection. If the line is parallel to the circle, there will be no points of intersection.

5. Can I use a calculator or computer program to find the point of intersection?

Yes, you can use a calculator or computer program to find the point of intersection. Many graphing calculators have built-in functions for finding the point of intersection of a line and a circle. There are also online calculators and computer programs available that can solve for the point of intersection for you.

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