Circle Equations

Question 1

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

Answer 1

X² + y² = r²

Where r is the radius

Question 2

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

Answer 2

(X-a)² + (y-b)² = r²

Where r is the radius
Where (a,b) is the center

Question 3

If the equation of a circle is given in the form:
X² + y² +2fx +2gy +c = 0
How do you change it to a normal circle equation form?

Answer 3

COMPLETE THE SQUARE

х² + y² + 2fх + 2gy + c = 0
(х+f)² - (f)² + (y+g)² - (y)² + c = 0

(X+f)² + (y+g)² = √ f² + y² - c

Question 4

Which bit of a circle equation tells you the centre of the circle?

Answer 4

(X-a)² + (y-b)² = r²

(A , b) is centre
So the opposite sign to what is inside the bracket for the number inside the bracket.

Question 5

What is the part of a circle equation which tells you the radius?

Answer 5

(X-a)² + (y-b)² = r²

R is the radius
So square root the answer to find it.