Equation of a circle
Finding the centre and radius
Axes intercepts
Coordinate geometry
Circle inequalities and problem solving
100
Find the equation of a circle with centre (3,-2) and radius 5 units. Give in centre-radius form.
(x-3)^2+(x+2)^2=25
100
Find the centre and radius of the circle with equation (x-8)^2+(y+1)^2=7
Centre (8,-1)
Radius sqrt7
100
Find the x and y intercepts of the circle with equation x^2+y^2=10
(sqrt10, 0) ,(-sqrt10,0),(0,sqrt10) and (0, -sqrt10)
100
Find the radius of the circle shown.
sqrt26
100
Consider (x-2)^2+(y-5)^2 <=8 . Does the point (4.4, 3.1) lie inside or outside of this region?
Outside.
Substitute point into the LHS of the circle equation.
9.37>8
200
Find the equation of a circle with centre (0,7) and radius sqrt3 . Give in centre-radius form.
x^2+(y-7)^2=3
200
Find the centre and radius of the circle with equation x^2+y^2+10x-6y+30=0
Centre (-5,3)
Radius 2
200
Find the x intercepts of the circle with equation x^2+y^2+4x-11y-12=0
(2,0) and (-6,0)
200
Find, in centre-radius form, the equation of a circle, with centre (1,2) and which passes through (3,5)
(x-1)^2+(y-2)^2=13
200
Write down the inequality that represents the region shown.
x^2+(y-1)^2<16
300
Find, in general form, the equation of the circle shown.
x^2+y^2-4x-2y-4=0
300
Does the point (14,8) lie on the circle that is centred at the origin and has a diameter of 32 units? Prove your answer.
No.
The radius of the circle is 16.
The distance from (0,0) to (14,8) is 2sqrt65approx16.1 which is not 16.
OR the equation of the circle is
x^2+y^2=16^2
x^2+y^2=256
Substituting (14, 8)
14^2+8^2=196+64=260 which does not equal 256
300
Find the y intercepts of the circle with equation x^2+y^2+2x-8=0
(0,-2sqrt2) and (0,2sqrt2)
300
Find, in centre-radius form, the equation of a circle which has a diameter with endpoints (7,4) and (-1,-2)
(x-3)^2+(y-1)^2=25
300
Flora's flower shop is located at grid reference (3,4) where each grid unit equals 2 km. The shop charges $7.50 extra for deliveries 10 km beyond the shop. Write an inequality to describe the region where the extra delivery charge is applied.
(x-3)^2+(y-4)^2>25
400
Find, in general form, the equation of the circle with centre (-4,5) and which touches the x axis.
x^2+y^2+8x-10y+16=0
400
The circle shown has a centre (h,k) and a radius of 5. What are the coordinates of the centre of the circle?
(3,7)
400
Find the x intercepts of the circle with equation x^2+y^2-6x-4y-5=0
400
Consider the circle with equation (x+9)^2+(y-4)^2=200 . Find the equation of the tangent to the circle at (1,-6) .
y=x-7
400
A satellite dish has a broadcast region defined by the inequality x^2+y^2+10x+14y+38<=0 . Find the grid location of the satellite dish and its broadcasting radius.
(-5,-7)
Radius = 6 km