11.04 Circles (Extended)
State the equations of the circles below:
For each of the following circles:
Write the coordinates of the centre.
Find the radius of the circle.
Find the x-intercepts.
Find the y-intercepts.
Sketch the graph of the circle.
For each of the following circles:
Write the equation of the circle.
Sketch the graph of the circle.
A circle that has its centre at the origin and a radius of 9 units.
A circle that has its centre at the origin and a radius of 4 units.
A circle that has its centre at the origin and a radius of \sqrt{18} units.
A circle that has its centre at the origin and a radius of \sqrt{3} units.
A circle that has its centre at the origin and a radius of 7 units.
Consider the circle with equation x^{2} + y^{2} = 121.
Find the diameter of the circle.
Find the y-values of the points on the circle that have an x-coordinate of -6.
Consider the circle with centre (0, 0) that passes through the point (5, - 10).
Find the radius of the circle.
Find the equation of the circle.
A circle with centre \left(0, 0\right) has an x-intercept at \left(6, 0\right).
Find the equation of the circle.
Find the exact area enclosed by the circle.
Does the point (- 4, 2) lie inside, outside or on the circle x^{2} + y^{2} = 21?
Does the point ( 3, 5) lie inside, outside or on the circle x^{2} + y^{2} = 5?
Does the point (0, -7) lie inside, outside or on the circle x^{2} + y^{2} = 49?
A circle has the equation 25 x^{2} + 25 y^{2} = 400.
Find the coordinates for the centre of the circle.
State the radius of the circle.
Hence, sketch the graph of the circle: 25 x^{2} + 25 y^{2} = 400.
A circle has the equation 3 x^{2} + 3 y^{2} - 48 = 0.
Find the coordinates for the centre of the circle.
State the radius of the circle.
Hence, sketch the graph of the circle: 3 x^{2} + 3 y^{2} - 48 = 0.
For each of the following pairs of graphs, describe how the graph in Diagram 1 is translated to the position shown in Diagram 2:
Diagram 1
Diagram 2
Diagram 1
Diagram 2
Diagram 1
Diagram 2
Diagram 1
Diagram 2
How many units away from the origin have the circles below been translated?
\left(x + 5\right)^{2} + y^{2} = 4
x^{2} + \left(y - 7\right)^{2} = 6^{2}
Consider the graph of the circle below:
Describe the translation to get from x^{2} + y^{2} = 5^{2} to the circle shown.
State the equation of the circle shown in the graph.
Find the coordinates of the new center after a circle centered at the origin is translated as follows:
2 units downwards.
7 units upwards.
3 units to the left.
6 units to the right.
Write down the equation of the new circle after x^{2} + y^{2} = 49 is translated:
5 units upwards.
5 units downwards.
5 units to the right.
5 units to the left and 6 units upwards.
A circle of radius 7 which was initially centred at the origin has been translated 6 units downwards.
State the radius of the resulting circle.
State the centre of the resulting circle.
Write the equation of the resulting circle.
Given the graph of x^{2} + y^{2} = 6^{2}, sketch the graph of x^{2} + \left(y - 3\right)^{2} = 6^{2}.
Given the graph of x^{2} + y^{2} = 4^{2}, sketch the graph of x^{2} + \left(y + 6\right)^{2} = 4^{2}.
A circle of radius 7, centred at the origin, is translated 9 units vertically downwards.
Write the equation of the resulting circle.
Graph the following translated circles as follows:
The circle x^{2} + y^{2} = 4^{2} is translated 4 units down.
The circle x^{2} + y^{2} = 25 is translated horizontally 4 units to the left.
Consider the circle with equation \left(x - 3\right)^{2} + y^{2} = 36.
Find the coordinates of the centre.
State the radius of the circle.
Graph the circles defined by the following equations:
x^{2} + \left(y - 2\right)^{2} = 4^{2}
x^{2} + \left(y + 6\right)^{2} = 5^{2}
\left(x - 3\right)^{2} + y^{2} = 25
\left(x + 5\right)^{2} + y^{2} = 16
\left(x - 4\right)^{2} + y^{2} = 9
\left(x + 4\right)^{2} + y^{2} = 25