Given the equation of a circle x^{2} + y^{2} = 64:
For each of the following circles:
Write down the equation for a circle with centre \left(0, 0\right) and radius 2.
The equation of a circle is given by x^{2} + y^{2} = 32. Calculate the radius of this circle, writing your answer in simplest surd form.
Consider the graph of the circle shown below.
State the following in interval notation.
The domain
The range
Consider the circle with centre (0, 0) that passes through the point (5, - 10).
Find the exact 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 inside the circle.
Consider the circle with equation x^{2} + y^{2} = 49.
What is the diameter of the circle?
Find the y-values of the points on the circle that have an x-coordinates of 1.
Sketch the graph of x^{2} + y^{2} = 3.
Does the point (- 4, 2) lie inside, outside or on the circle x^{2} + y^{2} = 21?
A circle has the equation 25 x^{2} + 25 y^{2} = 400.
What are the coordinates of the centre of the circle?
State the radius of the circle.
Sketch the curve of 25 x^{2} + 25 y^{2} = 400.
Determine whether the following are equations of circles.
\left(x + y\right)^{2} = 4
4 x^{2} + 5 y^{2} = 4
y^{2} = 2 + x^{2}
4 x^{2} + 4 y^{2} = 16
x^{2} + y^{2} = 4
y^{2} = 2 - x^{2}
Consider a circle with centre at (3, 3) and radius of 6 units.
Given the equation of a circle x^{2} + \left(y - 3\right)^{2} = 9:
For each of the following circles:
Find the equation of a circle that has been translated 2 units downwards from the origin with radius of 5 units.
Consider the circle with centre (8, 6) and radius 8.
Write down the equation of the circle.
Does the circle pass through (0, 0)?
Does \left(x - 7\right)^{2} + \left(y - 5\right)^{2} = - 4 represent the equation of a circle?
Is the following statement true or false?
The graph of \left(x - 4\right) + \left(y + 3\right) = 4 is a circle with radius 2 and centre at \left(4, - 3 \right).
The equation of a circle is given by \left(x - 6\right)^{2} + \left(y - 6\right)^{2} = 12.
Find the coordinates of the centre.
Find the radius, in simplest surd form.
Consider the circle on the graph.
Find the centre of the circle.
Find the radius of the circle.
What is the equation of the circle?
Write the equation of the circle given the following centre and radius.
Centre \left(1, - 3 \right) and radius of 5 units.
Centre \left( - 5.7 , 0\right) and radius of 3 units.
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 centred at (7, - 8) has an x-intercept at (- 10, 0). Find the exact radius of the circle.
A circle is described by the following equation:
\left(x + \frac{1}{2}\right)^{2} + \left(y + \frac{1}{2}\right)^{2} = \frac{9}{4}
Find the centre of the circle.
Find the radius of the circle.
Plot the graph of the circle.
How many x-intercepts does the circle \left(x - 7\right)^{2} + \left(y - 1\right)^{2} = 4 have?
A circle has a domain of \left[2, 10\right] and a range of \left[ - 4 , 4\right].
Plot the circle.
State the equation for the circle
Consider the circle \left(x - 3\right)^{2} + \left(y + 1\right)^{2} = 9shown:
If this circle was inscribed (fitted exactly) inside a square so that the sides of the circle touched the sides of the square, state the coordinates of the following vertices of the square:
top-left vertex
top-right vertex
bottom-left vertex
bottom-right vertex
For each equation below, determine:
The equation of the circle in the form \left(x - h\right)^{2} + \left(y - k\right)^{2} = r^2.
The coordinates of the centre of the circle.
The radius of the circle.
Consider the equation of a circle given by x^{2} + 4 x + y^{2} - 10 y = 52.
Rewrite the equation of the circle in the form \left(x - h\right)^{2} + \left(y - k\right)^{2} = r^2.
What are the coordinates of the centre of the circle?
What is the radius of the circle?
Graph the circle.
Consider the equation of a circle given by x^{2} + y^{2} - 2 x - 10 y - 24 = 0.
Rewrite the equation of the circle in the form \left(x - h\right)^{2} + \left(y - k\right)^{2} = r^2.
What are the coordinates of the centre?
Find the radius in simplest surd form.
Find the y-intercepts.
Find the x-intercepts.
Graph the circle.
Consider the equation of a circle given by y^{2} + 2 y + 8 = 12 x - x^{2} + 7.
Rewrite the equation of the circle in the form \left(x - h\right)^{2} + \left(y - k\right)^{2} = r^2.
What are the coordinates of the centre of the circle?
What is the radius of the circle?
Graph the circle.
A circle has the equation x^{2} + y^{2} - 32 x + 30 y + 462 = 0.
Rearrange the equation into the form \left(x - h\right)^{2} + \left(y - k\right)^{2} = r^{2}.
State the domain of the circle in interval notation.
State the range of the circle in interval notation.
Determine whether the following points lie inside or outside the circle.
\left(10, - 15 \right)
\left(16, - 15 \right)
\left(16, -12\right)
\left(25, - 14 \right)
Graph the circle x^{2} + y^{2} - 6 x + 4 y = 3.
If a circle of radius 8 rolls along the x-axis, state an equation for the path of the centre of the circle.
For the following graphs of semicircles, find:
A semicircle has equation y = \sqrt{64 - x^{2}}.
State the centre of the semicircle.
State the radius of the semicircle.
Sketch the graph of y = \sqrt{64 - x^{2}}.
Is the function f \left( x \right) = - \sqrt{49 - x^{2}} one-to-one?
Consider the circle with equation x^{2} + y^{2} = 4.
Rearrange the equation to make y the subject.
Write down the equation of the semicircle which has a radius of 2 and negative y-values.
Draw the graph of the semicircle.
Consider the semicircle below:
Determine the domain of the function.
Determine the range of the function.
For each equation of a semicircle below:
Consider the graph of y = \sqrt{4 - x^{2}} shown.
Find the new equation if the semi-circle is translated:
Down by 7 units.
To the left by 3 units.
The top half of a circle has a domain of \left[ - 10 , 2\right] and a range of \left[ - 2 , 4\right].
Plot the semicircle.
State the equation of the semicircle.
A soccer match is being televised.
One of the cameras is mounted on a drone which is programmed to zoom in on the ball only when it is inside the centre circle.
The drone uses a coordinate system to track the position of the ball, where the origin is at the bottom left corner of the field and each unit corresponds to 1\text{ m}.
The centre of the centre circle is in the exact middle of the field.
What are the coordinates of the circle's centre?
What is the radius of the centre circle?
State the equation of the circle.
State the domain of the circle in interval notation.
State the range of the circle in interval notation.