Circles

Question 1

What is the equation of a circle with centre (0,0)

Answer 1

By Pythagoras:

x^2 + y^2 = r^2

Question 2

What is the equation of a circle with centre (a,b) ?

Answer 2

By Pythagoras
(x-a)^2 + (y-b)^2 = r^2

Question 3

Find the equation of a circle with centre (-2,3) and radius 2?

Answer 3

(x-(-2))^2 + (y-3)^2 = 2^2

(x+2)^2 + (y-3)^2 =2^2

Question 4

Find the centre and radius of a circle with equation

(x-3)^2 + (y+1)^2 =9

Answer 4

Centre = (3,-1)

Radius= square root of 9 =3

Question 5

Find the centre and radius of circle with equation

x^2+4x+y^2-6y-7=0

Answer 5

(x+2)^2-4+(y-3)^2-9-7=0
(x+2)^2+(y-3)^2=20
centre=(-2,3)
radius= square root of 20