- #1
Murtuza Tipu
- 49
- 2
General formula of a line is ax+b=0
Similarly can we have a general formula of a circle ?
Similarly can we have a general formula of a circle ?
What would be general formula of a circle in form of variables ?
In summary, the conversation discussed the general formulas for a line and a circle in a plane. The general formula for a line is y=mx+c and the general formula for a circle is x^2+y^2=r^2 (where r is the radius of the circle). It was also mentioned that there is a more general equation for a circle with a center not located at the origin.
- #2
HomogenousCow
- 737
- 213
The general formula for a line in a plane is y=mx+c
The general formula for a circle in the x-y plane is x^2+y^2=r^2 (where r is the radius of the circle)
The general formula for a circle in the x-y plane is x^2+y^2=r^2 (where r is the radius of the circle)
- #3
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
- 12,811
- 1,671
HomogenousCow said:
There's an even more general equation for a circle, one whose center is not located at the origin.
1. What is the general formula of a circle?
The general formula of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.
2. Can the general formula of a circle be expressed in terms of variables?
Yes, the general formula of a circle can be expressed in terms of variables, as shown in the formula (x - h)^2 + (y - k)^2 = r^2.
3. Why is the general formula of a circle expressed in terms of variables?
The general formula of a circle is expressed in terms of variables because it allows for any circle to be represented regardless of its size or location on a coordinate plane.
4. What do the variables in the general formula of a circle represent?
The variables in the general formula of a circle represent the coordinates of the center of the circle (h, k) and the radius (r).
5. How is the general formula of a circle derived?
The general formula of a circle is derived from the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. By using this theorem and the distance formula, the general formula of a circle can be derived.
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