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The document illustrates the center-radius form of the equation of a circle, providing examples of writing the equation of circles given their center and radius. It then provides exercises for writing the standard form equation of various circles described by their center and radius.
•find the centre and radius of a circle, given its equation in standard form; •find the equation of the tangent to a circle through a given point on its circumference; •decide whether a given line is tangent to a given circle.
Example: A circle with center at (3,4) and a radius of 6: Start with: (x−a) 2 + (y−b) 2 = r 2. Put in (a,b) and r: (x−3) 2 + (y−4) 2 = 6 2. We can then use our algebra skills to simplify and rearrange that equation, depending on what we need it for.
The obvious characteristic of a circle is that every point on its circumference is the same distance from the centre. This fixed distance is called the radius of the circle and is generally denoted by R or r or a. In coordinate geometry terms suppose (x, y) denotes the coordinates of a point.
Consider a circle with radius r and center (h, k). Write the Distance Formula to represent the distance. d between a point (x, y) on the circle and the center (h, k) of the circle. Then square each side of the Distance Formula equation.
A circle is the set of all points located a fixed distance from some fixed point. The fixed distance is called the radius of the circle. The fixed point is called the center of the circle.
Whereabouts a circle is drawn on graph paper depends on two things: i) It’s centre. ii) It’s radius. For the time being we will only consider circles whose radius is the origin (0, 0). What we must try to do is describe any point on the circumference of the circle.
