ANALYTICAL GEOMETRY
2
YZ
2
CIRCLE WITH CENTRE ORIGIN ✗ + =p
a circle with r =3 and centre to :o)
determine equation of Circle ( x2 + y
'
=
9)
2 2
CIRCLES NOT CENTERED AT THE ORIGIN ( x a) -
+ ( y b) -
=p
2
-
a and b are the centre of circle .
1. if we
multiply the bracket out we get the general form .
2- To reverse from general form to centre -
radius form , complete the square .
3. make the coefficient of the x2 term and the y ' term equal to 1 ,
so we take out 3 as a common
factor
4. complete the square
5. factorise each bracket on the LHS and add numbers on RHS
bracket RHS the radius
6. by solving and the
=
each the centre
gives you
EQUATION OF A TANGENT TO A CIRCLE y
=
Msc + c
'
determine the gradient of radius
•
determine the gradient of the tangent using Mi ✗ Me = -
I
Use a point of contact to find C.
-
FINDING THE LENGTH OF A TANGENT FROM AN EXTERNAL POINT
'
draw a diagram
-
Use a distance formula
-
use completion of squares to find coordinates of centre
pythagoras
-
, Collinear points
-
lie on same straight line -
:
have same
gradient
simultaneous Equations
calculate coordinates of P in graphs 20C
-39=-4 and
-129=5
•
x
Angle of Inclination
inclination 10) is L between line and positive x-axis .
• measured in anti clockwise direction
-
Eg tano :O tan 1. m
-
.
m= so :
m ≥0
=
shifts tan
'
tan
- '
m≤ 0 :O =
.
m -1180
>
•
↑ °
< $ ☆
3, ×
L S
lb 1 N ES GRADIENT INCLINATION
-
acute
Positive '
-
( O -90)
-
Obtuse
negative .
(90-180)
0 0° inclination
90°
undefined
RIANGLES special lines
1 I
EDIAN :
line from a vertex Ofa to midpoint ofopp .
side
ALTITUDE :
line drawn from a vertex of a .
.
,
1- toopp side .
PERPENDICULAR BISECTOR : line that passes
through midpoint of the line segment and is to the
line segment .
I 1
2
YZ
2
CIRCLE WITH CENTRE ORIGIN ✗ + =p
a circle with r =3 and centre to :o)
determine equation of Circle ( x2 + y
'
=
9)
2 2
CIRCLES NOT CENTERED AT THE ORIGIN ( x a) -
+ ( y b) -
=p
2
-
a and b are the centre of circle .
1. if we
multiply the bracket out we get the general form .
2- To reverse from general form to centre -
radius form , complete the square .
3. make the coefficient of the x2 term and the y ' term equal to 1 ,
so we take out 3 as a common
factor
4. complete the square
5. factorise each bracket on the LHS and add numbers on RHS
bracket RHS the radius
6. by solving and the
=
each the centre
gives you
EQUATION OF A TANGENT TO A CIRCLE y
=
Msc + c
'
determine the gradient of radius
•
determine the gradient of the tangent using Mi ✗ Me = -
I
Use a point of contact to find C.
-
FINDING THE LENGTH OF A TANGENT FROM AN EXTERNAL POINT
'
draw a diagram
-
Use a distance formula
-
use completion of squares to find coordinates of centre
pythagoras
-
, Collinear points
-
lie on same straight line -
:
have same
gradient
simultaneous Equations
calculate coordinates of P in graphs 20C
-39=-4 and
-129=5
•
x
Angle of Inclination
inclination 10) is L between line and positive x-axis .
• measured in anti clockwise direction
-
Eg tano :O tan 1. m
-
.
m= so :
m ≥0
=
shifts tan
'
tan
- '
m≤ 0 :O =
.
m -1180
>
•
↑ °
< $ ☆
3, ×
L S
lb 1 N ES GRADIENT INCLINATION
-
acute
Positive '
-
( O -90)
-
Obtuse
negative .
(90-180)
0 0° inclination
90°
undefined
RIANGLES special lines
1 I
EDIAN :
line from a vertex Ofa to midpoint ofopp .
side
ALTITUDE :
line drawn from a vertex of a .
.
,
1- toopp side .
PERPENDICULAR BISECTOR : line that passes
through midpoint of the line segment and is to the
line segment .
I 1
