Key a-level facts

A perpendicular chord must go through the centre of a circle if…

1. Goes through the centre
2. Perpendicular
3. Bisector

If 2 are true then the 3rd will automatically be true

What is the equation of a circle not in the centre?

( x-a)*2 + ( y-b)2= r*\*2

How do you find the midpoint of two coordinates ?

X1+x2/ 2 and y1+y2/2

How do you find the distance between coordinates?

What does the discriminant look like if it has only 2 solutions?

b*2 -4ac > 0

What does the discriminant look like if it has only 1 solutions?

b*2 -4ac = 0

What does the discriminant look like if it has no solutions?

b*2-4ac < 0

If the gradient of two lines are perpendicular then …

M1 * M2 = -1