2024 cssa Q32 HELP PLEASEEE (1 Viewer)

[yourbestfriend]

Hey, can someone please help me figure out part b of Question 32 before my exam tmrw! I found out part a using the discriminant, but am so lost for part b
thank you!

 

[coolcat6778]

A level paper ahh question

 

[coolcat6778]

BEST MATH TRIAL PAPERS?

hey guys i was wondering if anyone had some high quality math advanced trial papers, notably from the prep companies? any help would be much appreciated :)

boredofstudies.org

 

[C2H6O]

View attachment 48623

View attachment 48624

Hey, can someone please help me figure out part b of Question 32 before my exam tmrw! I found out part a using the discriminant, but am so lost for part b
thank you!

ok first step is to break this down visually. we have a circle centered at (1, 3) with radius 3, and a diagonal line at 45 degrees that cuts the circle in two, such that the chord is of length 2root3

there are 2 possible values for d

adding in additional info, we can add to the diagram:

(i probably shouldnt have made A and B sitting on perfect coordinates but oh well)

using pythag you know the line PQ has to be of length root6, and perfectly diagonal.
im going to try find the green line so d1
all i need is the coordinates for Q, which working from the fact that PQ is diagonal and length root 6, using pythag, Q = (1+root3, 3-root3)

equation for line can be found using point gradient form, given that the gradient is 1, to be

rearrange and you get

and

there's probably cleaner solutions but its just a habit of mine to work geometrically to avoid algebraic clutter
also someone lmk if im wrong

edit: just realised this solution probably doesnt satisfy the criteria of find the coordinates of a and b. will come back to this later today if i get the chance, but if anyone else can do it quicker please help

 

[C2H6O]

Ok having looked over the algebraic options available and some asking around, I think this may be a badly worded question, as to logically find the coordinates of A and B you would need d first, or really unnecessary vector workarounds (done geometrically, similar to the method I prescribed above but using almost vector like calculations). Any solution which involves first finding the values of A and B would be redundant compared to a simple algebraic or geometric method. The method I have shown is the shortest I could find, and this is also a result of my preference to work geometrically. The algebraic alternative of this same solution would be to sub the line equation into the circle and solve from there, using the given length of the chord, but as you can see that gets much more complicated than a geometric solution which I have not fully resolved.

also idk why I’m talking so formally all of a sudden