#### MiseryParade

##### Active Member

- Joined
- Nov 29, 2011

- Messages
- 155

- Gender
- Female

- HSC
- 2013

a) Show that every circle that passes through the intersections of the circle x^2 + y^2 = 2 and the straight line y=x can be written in the form (x-μ)^2 + (y+μ)^2 = 2(1+μ^2).

b) Hence find the equation of such a circle which also passes through (4, -1).

+ question 2!

Suppose that a regular polygon has 'n' sides of length 1.

a) What will be the length of the side of the regular polygon with 2n sides that is formed by cutting off the vertices of the given polygon?

b) Confirm your answer in the case of:

i. cutting the corners off an equilateral triangle to form a regular hexagon

ii. Cutting the corners off a square to form a regular octagon

last question that isn't really a question: what abbreviations are you allowed to use in senior school? Teachers want us to write opposite instead of opp and straight instead of str, but are you allowed to use the angle symbol and the = symbol to write a proof?