Maths Paper 2 (Geometry) Summarized notes

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