a level circles

[raw osprey]

Hey i dont get part b at all!! Could use some help looked at the mark scheme but didnt get it at all

[olive pebble]

well so

if its a tangent to the circle

what would you expect to see from the solutions of your quadratic

since your quadratic tells you all the times they intersect

[raw osprey]

Thered be 1 solution

[olive pebble]

mmm exactly

now have you heard of something called the 'discriminant'

[raw osprey]

b2-4ac right

[olive pebble]

exactly

now how does that

what does that tell you

[raw osprey]

Im not too sure ive seen tlmaths use it and looking at it being greater than 0 or less than or something

But i dont get that at all lol

[olive pebble]

ok so

as you probably know

b^2 - 4ac is in the quadratic formula

right

[raw osprey]

Yep

[olive pebble]

in fact its +/- sqrt(that)

[raw osprey]

Right

[olive pebble]

now if you imagine that

b^2 - 4ac was some positive number

then when you plug it in

youd add and subtract some number right

in the formula

so your two solutions would be different numbers

right?

[raw osprey]

Right

[olive pebble]

aka if b^2 - 4ac > 0

your quadratic gives 2 solutions

[raw osprey]

Right

[olive pebble]

now what if b^2 - 4ac was 0

[raw osprey]

So if its 0 theres 1 solutiom

[olive pebble]

well then when you square root and do +/-

well it doesnt change

exactly

and if its negative

well sqrt(negative) doesnt work

so you have no solutions

now in your case you want 1 solution

[raw osprey]

Yes so you make it equal to 0

Would the a

a be 5
b be 4k and c (k^2-5)

Then youd use the discriminant make it equal to 0 and solve for k?

[olive pebble]

yeah that looks good

[raw osprey]

Alright one sec

Right so i got the solutions k=5 and k=-5

And id just use both as solutions for k right

[olive pebble]

and you can check they only give one solution if you want to

yep both are good

[raw osprey]

Ah right one sec then

Yep both give 0

Thanks for the help,, i saw him use the discriminant and completely skipped it thinking it wouldnt be relevant to my spec 🤣🤣

[olive pebble]

you pranked yourself

no worries

[raw osprey]

Haha thanks, have a good one