circle question help

was hoping someone could hint at how to start with answering the question below without giving too much away?

Screenshot 2024-04-07 172609.png

(edited 9 months ago)

Reply 1

mqb2766

You can work out the centre and radius of C2 and you know know how far C1's centre is from the C2 centre and you know the x coordinate so ..

Reply 2

million.

@mqb2766
with c2's equation would it be fine to just add the 32 to find the radius, since when you expand the (x-x1)^2 + (y-y1)^2 you woudl collect the whole numbers if that makes sense? so i woudlnt exactly be able to factorise it

i have the cnetre for c1 tho which would be (4,-k) and the distance of the centres/radius of c1 square root 45 just dk where to go from there

a pic of what i tried doing but it kinda became a mess

my workings

(edited 9 months ago)

Reply 3

username6691833

Substitute the coordinates of center of C2 into the equation for C1. For this you will first have to rewrite the equation for C2 in the standard form.

Reply 4

mqb2766

Original post by million.

@mqb2766
with c2's equation would it be fine to just add the 32 to find the radius, since when you expand the (x-x1)^2 + (y-y1)^2 you woudl collect the whole numbers if that makes sense? so i woudlnt exactly be able to factorise it
i have the cnetre for c1 tho which would be (4,-k) and the distance of the centres/radius of c1 square root 45 just dk where to go from there
a pic of what i tried doing but it kinda became a mess

Youd complete the square in both x and y to get the centre and radius for C2. Then k lies on the line x=4 at a distance C1 radius from the centre of C2 so you have two simultaneous equations.

Reply 5

million.

Original post by WordsFiddle

Substitute the coordinates of center of C2 into the equation for C1. For this you will first have to rewrite the equation for C2 in the standard form.

woudl the standard form be:

(x-1)^2 + (y-3)^2 = 42

Reply 6

username6691833

Original post by million.

woudl the standard form be:
(x-1)^2 + (y-3)^2 = 42

yup....but 36 instead of 42 i guess (you won't need it tho)

Reply 7

million.

Original post by WordsFiddle

yup....but 36 instead of 42 i guess (you won't need it tho)

can i ask why it would be 36 (just thought it would be useful to know where i make mistakes), when i completed the square i got -1 and then -9 outside the brackets then added it over to 32?

thank you for the help btw!

Reply 8

mqb2766

Original post by million.

42 is good, but as above its not important for the question.

Reply 9

million.

Original post by mqb2766

42 is good, but as above its not important for the question.

tysm for the help! i stil got the answer wrong when i entered the answer i ended up with, but ik where i went wrong ig.

Reply 10

mqb2766

Original post by million.

tysm for the help! i stil got the answer wrong when i entered the answer i ended up with, but ik where i went wrong ig.

It looks like the numbers have been chosen to make the calculation of k "easy" so you should be able to spot the value when you sub the other centre into the circle equation.