Circle Equations
3 forms of the equation
Transformational Form:
Standard Form:
General Form:
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Example 1: Find the centre and the radius, sketch the circle and then change the equation into standard and general form.
Example 2: Find the centre and the radius, sketch the circle and then change the equation into standard and general form.
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Example 3: Determine the centre and radius for each of the following
(x ­ 4)2 + (y + 5)2 = 36
centre (4, ­5) r = 6
(x + 9)2 + (y ­ 3)2 = 14
centre (­9, 3) r =√14
Example 4: Give the equation of the circle in standard form with a radius of 4 units and a centre (­3, 6).
(x + 3)2 + (y ­ 6)2 = 16
Example 5: Give the equation of the circle in standard form with a radius of √11 units and a centre (13, 0).
(x ­ 13)2 + y2 = 11
Example 6:
Give the centre and radius, then sketch the graph of:
x2 + y2 + 6x ­ 10y ­ 12 = 0
Change from general to standard form (Completing the Square)
1. collect x terms, collect y terms
2. create our brackets
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Mapping Notation
Example 7:
Give the centre, radius and mapping notation, then sketch the graph of:
x2 + y2 ­ 4x ­ 2y + 5 = 0
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Example 8:
Give the centre, radius and mapping notation, then sketch the graph of:
2x2 + 2y2 ­ 8x ­ 4y ­ 12 = 0
Example 9:
Give the centre, radius and mapping notation, then sketch the graph of:
3x2 + 3y2 + 12x ­ 18y ­ 23 = 0
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Example 10:
Give the centre, radius and mapping notation, then sketch the graph of:
x2 + y2 + 9x ­ 5y ­ 7 = 0
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