Equation of a circle
Finding the centre and radius
Axes intercepts
Coordinate geometry
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
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=11
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
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