Circle Theorems

Question 1

What is the equation of the circle?

Answer 1

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

Question 2

What is the centre of the circle?

Answer 2

(a,b)

Question 3

How do you derive the equation of the circle?

Answer 3

Complete the square

Question 4

How to find the radius with the centre and coordinates on the circle?

Answer 4

Find the difference between both points, sub into Pythagoras’ theorem and then find r.

Question 5

If the co ordinate is negative i.e (-a,-b) , what is the equation of the circle?

Answer 5

(x+a)^2 + (y+b)^2 = r^2

Question 6

What is the gradient of the tangent of the circle in terms of the normal?

Answer 6

Negative reciprocal (-1/m)

Question 7

The shortest distance from the centre of a circle to a chord is always the

Answer 7

perpendicular bisector

Question 8

Perpendicular bisectors always pass through the…

Answer 8

centre

BIsector it’s in the name!

Question 9

How to find the centre of a circle when given any three points on the circumference

Answer 9

.