Sudanese
Sudanese secondary
secondary school
school
MathMath
(LIMITS
IN )EXAMINATION )
( circle
MrMr:
: Altahir
Ahmed
0912473546
altahir
ahmed
0912473546
The CirCle
As the set of all points on the
plane which are equidistance
from a given point
If the set point of circle of
radius r is denoted by the
symbol n and its center by c
and A(x , y )
Any point on the circle . then characteristic
Of the circle is
N = { A (x , y ) : AC = r }
Equation of a circle given its center
and radius
( x- d )2 + ( y - h )2 = r2
Find the equation of the circle
whose center is the point (5 , -3 )
and which passes thruogh the
point ( 2 , 1)
Find the equation of the circle
whose center is the point (1 , -3 )
and the length of its radius equals
5 unit (( write the equation in the
general form ))
Find the equation of the circle
whose center is the point (2 , 3 )
and which touches the line
3x + 4y - 8 = 0
Math (
1
)
MR: ALTAHIR AHMED 0912473546
General form of The
equaTion of CirCle
x2 + y2 + 2gx + 2fy + c = 0
Find the center and the radius in
the center ( - g , - f )
following equations of circle
the radius r =√ g2 + f 2 - c
1 ) (x – 2)2 + (y + 3 ) 2 = 9
conditions and notes for equation
of the circle
1) the cofficient x2 = the
cofficient y2
2) it does not include the term xy
2
2
1 ) x + (y + 5 ) = 6
3) it is quadratic equation
4) If g2 + f 2 – c = 0 then the
equation represent a unique point
. but If g2 + f 2 – c < 0 then the
equation does not represent a
C ircle and its soluation is ∅
The center =
(
- Cofficient x
2
,
- Cofficient y
2
)
1 ) x2 + y 2 = 16
Which the equations of the
following represent a equation of
the circle and then find centre and
radius
1 ) x2 - y 2 = 6
Math (
)
2
MR: ALTAHIR AHMED 0912473546
1 ) 4x2 + 4y2+ 8x + 12y - 4 = 0
The equation of the circle
that passes through two
points and its cintre lies on
a given straigh line
1 ) x2 + y2+ 4x + 2y + 20 = 0
Find the equation of the circle that
passes through the points (0,0)
, (3,1)
and its centre lies on the
straight line x – y + 1 = 0
The equation of the circle
that passes through 3 points
Find the equation of the circle that
passes through the points :
(0,0) , (4,2) (2 , -4 )
The equation of the circle
given the end points of its
diameters :
( x – x1 ) ( x - x2 ) + ( y – y1 ) ( y - y2 ) = 0
Find the equation of the circle for
which the the end of the diameter
are (-2, 4 ) , (-1 , -5 )
Math (
)
3
MR: ALTAHIR AHMED 0912473546
The length a tangent drawn
to the circle from an
external points
The tangent of the circle
Find the length of the tangent from
drawn to the circle
x2 + y2 + 4x – 6y +5 = 0
from the point (2 , 1)
The equation of the tangent
( given point on the circle(x1
, y1 ) )
Find The equation of the tangent to
the circle
2x2 + 2y2 + 8x – 12y +2 = 0
from the point (2 , 1)
Check that the point ( 2 , -3 ) lies
on the circle :
x2 + y2 + 3x – 6y +2 = 0
and Find The equation of the
tangent drawn to it this point
Math (
4
)
MR: ALTAHIR AHMED 0912473546
