a) Write the coordinates of the points where the circle cut the x-axis.
b) Write the coordinate of the points where the circle cut the y-axis.
c) What is the y coordinate of a point on the circle having x-coordinate 3?
Doubt by Krishna Kripa
Solution :
Coordinates of the centre of circle (O) = (0,0)
Radius of the circle = 5 units.
a) Write the coordinates of the points where the circle cut the x-axis.
We know,
On x-axis, every y-coordinate is equal to zero and radius of the circle is 5 units. so the required coordinate of the point where the circle cuts the x-axis will be (5,0)
On x-axis, every y-coordinate is equal to zero and radius of the circle is 5 units. so the required coordinate of the point where the circle cuts the x-axis will be (5,0)
b) Write the coordinate of the points where the circle cut the y-axis.
We know,
On y-axis, every x-coordinate is equal to zero and radius of the circle is 5 units. so the required coordinate of the point where the circle cuts the y-axis will be (0,5)
c) What is the y coordinate of a point on the circle having x-coordinate 3?
We know,
Distance of any coordinate (x,y) from the origin (0,0) is given by √(x²+y²)
Distance of any coordinate (x,y) from the origin (0,0) is given by √(x²+y²)
Here
r = 5 units
x = 3
x = 3
y = ?
r=√(x²+y²)
SBS
r²=x²+y²
(5)²=(3)²+y²
25=9+y²
25-9=y²
16=y²
y²=16
y=±√16
(5)²=(3)²+y²
25=9+y²
25-9=y²
16=y²
y²=16
y=±√16
y=±4
y=+4 or -4
y=+4 or -4
Hence, the required y-coordinate on the circle must be either 4 or -4 when x coordinate is 3.