in a circle of radius 5cm centred on the point with coordinates (-2, 3) find the coordinates of points where circle cuts the x axis check whether (0,6) is a point on the circle
Answers
Answer:
Step-by-step explanation:
Perpendicular drawn from centre of the circle on the chord of the circle bisects the cord.
CP is the perpendicular drawn from centre C on cord OX.
OP=
2
1
OA=
2
1
8
2
+0
2
=4
OP=4
Point P lies on x axis so its y coordinate is 0.
Let (x,0) be the coordinates of P.
OP=
(x−0)
2
+(0−0)
2
=4
x
2
=16
x=4
Coordinates of point P are (4,0).
In △OPC using pythagoras theorem
OC
2
=CP
2
+OP
2
CP
2
=OC
2
−OP
2
CP
2
=5
2
−4
2
CP=3
Coordinates of point C are (4,3).
Draw CE perpendicular on chord OB.
Then y coordinate of point E and C are same.
Also x coordinate of point E is 0.
So coordinates of point E are (0,3).
Perpendicular drawn from centre of the circle on the chord of the circle bisects the chord.
OB=2OE=
0
2
+3
2
=6
OB=6
Point B lies on y axis so its x coordinate is 0.
Let (0,y) be the coordinates of B.
OB=
(0−0)
2
−(y−0)
2
=6
y
2
=36
y=6
Coordinates of point B are (0,6).