seems so light but i dont get it | Revision Server | Page 1

#

gather the x terms together

#

so you get x²-10x + y² = 6

#

we've moved the 6 onto RHS cus we need stuff in the form
(x-a)²+(y-b)²=r²

#

so now how can we get it more into the form we need?

#

you need to complete the square on the (x-5)² part

#

completing the square with x²-10x will give you (x-5)²-25

#

well what would be the centre of a circle with equation x²+y²=r²

#

thinking back to gcse

#

??

#

it's just (0,0)

#

because it's (x-0)²+(y-0)²=r²

#

so you get

#

x²+y²=r²

#

yeah

#

now finish it off

#

yep

#

that's exactly what I mean

#

always just go back to the form you need to get it to

#

now since the RHS represents r²

#

r² = 31

#

so what's r?

#

yep

#

now since we have it in the form (x-a)²+(y-b)²

#

the idea is

#

you swap the sign of the a and b values

#

and that's the centre

#

b is just 0

#

0² is still 0

#

wdym how?

#

because it's just y²

#

the only way to get just y²

#

is to have it as (y-0)²

#

which expanded is

#

y²-0y-0

#

which is y²

#

so you just get back to y² regardless

#

we write it exactly like that

#

but our radius is not 31

#

radius² is 31

#

exactly, no problem

#

sketch the circle

#

and you'll see

#

have a go

#

think about how the radius affects it

#

exactly, you just gotta say that distance from centre < sqrt(31)

#

hence the triangles vertex lies in the circle

#

this exact style of q came up in my actual a level lol

#

it was literally just the 11 (a) and 11 (b) (i) so yeah

#

well it's more than that

#

you gotta use some algebra

#

since it's 4 marks worth

#

they haven't gave you x=8

#

and a diagram

#

for no reason

#

try using angle facts

#

and go from there

#

see if inspiration strikes

#

you need to find the other two vertices of that triangle

#

then find the distance from centre to each of the vertices

#

if the vertices lie in the circle, then the whole triangle does

#seems so light but i dont get it