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Revision of Coordinate Geometry
1
January 12, 2013
The Circle
Revision
14 Jan 2013
The Line and
Revision of Coordinate Geometry
2
January 12, 2013Coordinate geometry of the circle assumes knowledge of coordinate geometry of the line.
Coordinate Geometry of The Line
Midpoint (average point)
slope (given 2 points)
slope (given graph)
parallel slopes
perpendicular slopes
distance between 2 points
from Junior Cent
Rise
Run
Rise
Run
slope (given ax + by+ c = 0)
Slope from equation of line
Slope from equation of line
slope (given: y = mx + c)
equation of a line
point of intersection of 2 lines
If (x1, y1) is on the line ax + by + c = 0 then ax1 + by1 + c = 0
Graph line(given ax + by+ c = 0)
(given: y = mx + c)Graph line
point on a line
Solve simultaneous equations
from Junior Cent
TransformationsImage of under...
axial symmetry
central symmetry
transformation
Revision of Coordinate Geometry
3
January 12, 2013
Coordinate Geometry of The LineLeaving Cert. Ordinary Level
Area of a circlewith vertex (0, 0)
(0, 0) not vertexArea of a circle ⇒ transform triangle so it has a vertex at (0, 0)
Internally divide a line segment in the ratio m:n
The angle between 2 lines
The perpendicular distance from a point to a line
can use ratios or formula
Leaving Cert. Higher Level
Diameter
The Circle Junior Cert. Geometry
Radius
Diameter
2r = d
Angle of 90o stands on diameter
Centre is midpoint of diameter
Diameter, radius
Area CircumferenceArea & Circumference
Sector
arc
chord
Segment
Perpendicular line from centre
through chord bisects chord
Tangent is perpendicular to line [ct]
Area of sector Arc length
c is midpoint of [ab]
Tangent
Angles standing on same arc
Revision of Coordinate Geometry
4
January 12, 2013
The Circle Leaving Cert. Ordinary Level
Equation of a circle
Points in, on, outside a circle Point inside circle Point on circle Point outside circle
Sub. point into the equation
Intersection of a line a circle Solve simultaneous equations
Proving a line is a tangent to a circle
Circle intersecting axes Intersects xaxis where y=0 Intersects yaxis where x=0
⇒ only 1 point of intersection
rewrite linear
sub into circle
solve quadratic
sub solutions into linear
also distance from c to T is r
The Circle Leaving Cert. Higher Level
General equation of a circle
Centre
Radius
Touching circles Touch externally Touch internally
Equation of tangent
or use formula in log tables
Common chord (or tangent)circles s1 and s2 expressed in the form
then
Circles touching axes touches xaxis touches yaxis