Circles
By DarthVader
Date: 2022-04-30
Topic: 102 see comments
Post views: 1147
Circles
Circumference of a circle:
Circumference = πd or 2πr
d = diameter
r = radius
Area of a circle:
Area = πr2 or ¼πd2
Equation of a circle:
(x − a)2 + (y − b)2 = r2
where:
(a, b) = center point of the circle
r = radius
Identifying equations of circles:
An equation of a circle can come in alternative forms in terms of x2, x, y2 and y. For example:
x2 + y2 + 4x − 12y − 9 = 0
It is NOT an equation of a circle if:
- The coefficients of x2 and y2 are different.
- The value of r2 is a negative square root i.e not a real number.
- The value of r2 is zero, which means the radius is a single point with no length.
To find the equation of a circle passing through three points:
- Find the equation of the perpendicular bisector of the line segment that joins any pair of the three points.
- Find the equation of the perpendicular bisector of the line segment that joins a different pair of the three points.
- Find the point of intersection of these two bisectors. This is the centre of the circle, (a, b).
- Find the distance from the center to any of the three points. This is the radius of the circle, r.
Hence substitute the values for a, b and r into the standard form of the equation of a circle.
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