1Which equation represents the circle with centre (0, 0) and radius 10 units: \( x^2 - y^2 = 10 \), \( x^2 + y^2 = 10 \), \( x^2 - y^2 = 100 \) or \( x^2 + y^2 = 100 \)?
2Which of the points (0, 0), (1, 0), (2, 1) and (0, 2) lies on the circle \( (x - 5)^2 + (y - 4)^2 = 18 \)?
3A circle with centre (0, 0) passes through (-8, -15). What is its radius: 8, 15, 17 or 21 units?
4What are the centre and radius of the circle \( x^2 + y^2 - 4x - 8y - 45 = 0 \)? Choose from: centre (2, 4) and radius 5 units; centre (4, 8) and radius 65 units; centre (4, 8) and radius \( \sqrt{65} \) units; centre (2, 4) and radius \( \sqrt{65} \) units.
5Which is the equation of the circle with centre (1, -2) and radius 4 units: \( (x + 1)^2 + (y - 2)^2 = 4^2 \), \( (x + 1)^2 + (y + 2)^2 = 4^2 \), \( (x - 1)^2 + (y - 2)^2 = 4^2 \) or \( (x - 1)^2 + (y + 2)^2 = 4^2 \)?
6Find the equation of the circle with centre (-4, 1) and radius 4 units.
7Find the equation of the circle with centre (-3, -4) and radius 7 units.
8Find the equation of the circle with centre (2, -1) and radius 3 units.
9Find the equation of the circle with centre (0, 10) and radius 5 units.
10Find the equation of the circle with centre (-a, -a) and radius \( a\sqrt{2} \) units.
11Find the equation of the circle with centre (a, b) and radius b units.
12Find the centre and radius of the circle \( x^2 + y^2 = 25 \).
13Find the centre and radius of the circle \( (x - 0)^2 + (y - 0)^2 = 36 \).
14Find the centre and radius of the circle \( (x - 0)^2 + (y + 2)^2 = 36 \).
15Find the centre and radius of the circle \( x^2 + y^2 - 2y = 24 \).
16Find the centre and radius of the circle \( x^2 + y^2 - 10x + 4y + 13 = 0 \).
17Find the centre and radius of the circle \( x^2 + y^2 + 6x - 8y - 11 = 0 \).
18Find the centre and radius of the circle \( 2x^2 + 2y^2 - 8x - 12y + 1 = 0 \).
19Find the centre and radius of the circle \( 9x^2 + 9y^2 - 36x + 6y - 107 = 0 \).
20The ends of a diameter of a circle are (a, -1) and (-a, 2). Find its equation.
21The ends of a diameter of a circle are (2, -6) and (3, -7). Find its equation.
22The ends of a diameter of a circle are (0, -7) and (-3, 2). Find its equation.
23The equation of a circle is \( x^2 + y^2 - 4x + 6y - 12 = 0 \). Find the coordinates of its centre. If one end of a diameter is (5, 3), find the coordinates of the other end.
24The equation of a circle is \( x^2 + y^2 - 6x - 8y - 11 = 0 \). Find its centre and radius. If one end of a diameter is (-2, -3), find the other end.
25The equation of a circle is \( 3x^2 + 3y^2 + 6x - 3y + 3 = 0 \). Find its centre and radius. If one end of a diameter is (5, 3), find the other end.
26Find the equation of the circle that lies wholly in the third quadrant, touches both axes and has radius 5 units.
27Find the equation of the circle that lies wholly in the fourth quadrant, touches both axes and has radius 6 units.
28Find the equation of the circle that passes through the origin with x-intercept 4 units and y-intercept 6 units.
29Find the equation of the circle that passes through the origin with x-intercept 5 units and y-intercept 10 units.
30Find the equation of the circle that passes through the origin with x-intercept 12 units and y-intercept 8 units.
31A circle passes through M(-2, 0) and N(0, -2), and its centre C(h, k) lies on the line 2x - 3y + 1 = 0. Find its equation.
32A circle passes through P(4, 1) and Q(6, 5), and its centre C(h, k) lies on the line 4x + y = 16. Find its equation.
33Find the equation of the circle passing through (0, 0), (4, 0) and (0, 2).
34Find the equation of the circle passing through (0, 0), (5, 0) and (0, 5).
35Find the equation of the circle that is concentric with \( x^2 + y^2 - 8x + 4 = 0 \) and passes through the point (4, 2).
36Find the equation of the circle with centre (-1, 2) that passes through the centre of the circle \( x^2 + y^2 - 6x - 10y - 2 = 0 \).
37A circular flower garden is made in the middle of a school playground. On a coordinate system its centre is taken as (2, -1) and its radius is 7 metres. Write the equation of the circle that represents the edge of the garden. Another student is standing at the point (8, -1). Is that student inside the garden, outside it or exactly on its edge? Explain with a reason.
38Why must the coefficients of \( x^2 \) and \( y^2 \) be made equal to 1 before comparing an equation with \( x^2 + y^2 + 2gx + 2fy + c = 0 \)?
39Find the equation of the circle with centre (2, 3) that touches the x-axis.
40Explain why the angle APB is 90° when AB is a diameter of a circle and P is any other point on it, and why this matters for the diameter form of the equation.