- The locus of a point that moves in a plane such that its distance from a fixed point is always constant is called a Circle.
- The fixed point is called the center, and the constant distance is called the circle's radius.
Central form of a circle:
- The equation of a circle with its center at C(h, k) and radius r units is given by:
Simplest form of a circle:
- If the center of a circle is at the origin, the equation of the circle reduces to its simplest form:
Question 1: Find the equation of a circle with its center at and having a radius of 9 units.
Here, , and units.
Equation of the circle:
Question 2: Identify the coordinates of the center and radius of a circle represented by the equation .
So, the center of the given circle is at (2, 5) and its radius is 4 units.
Question 3: Find the equation of a circle whose center is and which passes through the point .
Solution: The equation of the circle with the center and radius is:
Question 4: Find the equation of a circle whose diameters are and and the area is .
Solution: The point of intersection of the diameters and is . Thus the center of the circle will be at .
The radius of the circle can be found using the given area of the circle.
Therefore, the equation of the circle will be: .
- The equation of a circle with center and radius units is:
- Attention must be paid to the sign of numbers while substituting the values in the equation of the circle.