Equation of a Circle Passing Through Given Points

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In summary, the problem is to find the equation of a circle that passes through the y-axis and x-axis, as well as the point (8, -1). The equation should be in the form (x-h)^2+(y-k)^2=r^2. The difficulty lies in the fact that there are no other given points, but it is clarified that the circle is tangent to the axis lines. After some calculations, the possible radius values are 8.5 or 0.5, and the process involves using geometry in a Pythagorean triangle.
  • #1
furtivefelon
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hi, this isn't really a physics problem, more of a math problem, however, i can't find a math forum.. so i thought i'd put it here :D

your given that a circle passes through y-axis adn x-axis, also the circle passes through the points (8, -1).. find the equation of the circle, reminded that the equation should be in the following form: (x-h)^2+(y-k)^2=r^2

i have no idea how i should approach this problem, thanks a lot for your help :P
 
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  • #2
furtivefelon said:
your given that a circle passes through y-axis adn x-axis, also the circle passes through the points (8, -1)..

What are the other points?
 
  • #3
that's teh whole question.. that's suppose to be the hardest problem on the sheet, and since there are no any other point, i can't figure it out :|
 
  • #4
What do you mean my passes through "y" & "x" axis...?Shouldn't it be the other way around...?:wink: Actually,i think they mean that the circle is tangent to those lines...

I found the radius to be either 8.5,or 0.5.You decide which value is correct...

Daniel.
 
  • #5
mmm.. yes, it indeed is tangent to the x/y axis.. can you tell me how you got it? i care more about the process than the result :D thank you very much!
 
  • #6
Draw a circle & use geometry in a pythagoreic triangle...

Daniel.
 

1. What is the general equation for a circle?

The general equation for a circle is (x - h)^2 + (y - k)^2 = r^2, where (h,k) represents the center of the circle and r represents the radius.

2. How do you find the equation of a circle given its center and radius?

To find the equation of a circle when given its center (h,k) and radius r, simply plug these values into the general equation: (x - h)^2 + (y - k)^2 = r^2.

3. Can you find the equation of a circle if only given three points on its circumference?

Yes, it is possible to find the equation of a circle using three points on its circumference. First, use the distance formula to find the length of each side of the triangle formed by the three points. Then, use the formula (x - h)^2 + (y - k)^2 = r^2 and the coordinates of one of the points to create a system of equations. Solve for the center (h,k) and radius r, and then plug these values into the general equation.

4. How do you determine if a given equation represents a circle?

To determine if an equation represents a circle, check if the equation is in the form of (x - h)^2 + (y - k)^2 = r^2. If it is, then it represents a circle. If not, then it represents a different type of conic section.

5. Can the equation of a circle be written in standard form?

Yes, the equation of a circle can be written in standard form, which is (x - a)^2 + (y - b)^2 = r^2, where (a,b) represents the center of the circle and r represents the radius. This form is often used when graphing circles because it makes it easy to identify the center and radius of the circle.

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