A-Level Maths: C2-07 [Circles: Finding where Two Circles Intersect]

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[@RainbowTyrant]

You have legit just saved me so many tears thank you

[@jalajarora2331]

Great Video btw, Respect from a very frequent viewer!

[@puddleduck1405]

THANK YOU SO MUCH! I HAVE A MATHS TEST 1ST PERIOD. You're videos are amazing, God bless!

[@ai_serf]

this is a clinic in analytical geometry. beautiful, well done! the concrete algebra and calculutions of numbers was rigorous.

[@zaarifhossaini6467]

Thank you so much. I have my AS in May, haven't finished my whole syllabus yet but your videos are helping a lot :)

[@juliasmith1182]

Thank you for the video. If I may ask, are there any computational advantages using different methods. For instance, could you use the midpoint theorem and complex conjugation to construct the line, if it exists, that intersects the two circles? (Will ofc try myself haha...). Thanks again..

[@chillinglyrelaxing2260]

Fantastic i have an exam in 2 days i needed this . thank you

[@jamminermit]

Hi, would you be able to produce videos covering how to determine whether two circles are intersecting, disjointed, tangent, or if one circle is completely inside another(not actually finding the coordinates of any intersections)? The basic method is to find the distance between the centres and then compare this to the length of the radius to get the answer. This is stated at the end of the coordinate geometry section for OCR A. No worries if you can’t though, its just the topic was a little bit confusing. Thanks for your work!

[@TLMaths]

Here you are: kzbin.info/www/bejne/onXOkGume9-BkLs

[@mellowhead]

Do we assume that the circle would intersect at exactly 2 points? What if they only intersect at one - would the eventual quadratic only give us one value of x?

[@TLMaths]

If the circles intersect at two distinct points, then your quadratic will have two distinct real roots. If the circles intersect at one point, then your quadratic will have one repeated real root. If the circles don't intersect, then your quadratic will have no real roots.

[@PogbaMUFC6]

Hi, this video is marked as an extension but a question of this format appears in AQA practice paper set 1 paper 1

[@kevinodhiambo5796]

This is great i like the approach

[@file4318]

Amazing video thank you very much

[@samstephens891]

Thank you!

[@aristrait1808]

Hi. I think it's been covered before but I've forgotten. Why from the equation in the ()squaree form (around 5:20) can you not just square root everything? I'm guessing it's because it loses a solution but I'm not sure why x

[@sasharozanov4674]

If the equations were both equal to Y instead of zero (after you rearranged), could you have made them equal each other and then solved?

[@TLMaths]

Rearranging both of the equations to get y= leaves you with a fiddly equation to solve, but in general this should work. Best to keep an eye out for other methods if possible.

[@jackudygames90]

Hi Jack, Do your videos cover all of the content for the AQA A-level specification?

[@TLMaths]

Yes, when I’ve completed the playlist. All the exam boards now cover exactly the same content so there are no longer any differences apart from the large data set and how the material is spread over the exams.

[@sea5205]

Great video

[@dannynoller6835]

Hi Jack, why does subtracting one circle equation from the other yield the line going through the two points of intersection? I don't doubt that it works, it's just that it isn't intuitive to me. Also, could this be done using substitution instead of elimination? As a further point- I notice this topic is marked as an 'extension'. Is this so marked because such a topic is unlikely to arise in an exam, and this video is therefore to spark further interest? Or is it the case that 'extension' topics may be tested in exams?

[@TLMaths]

Hi Danny! You've got two equations involving x and y - when we treat them as simultaneous equations, the x and the y in both equations represent the coordinates of intersection. Subsequently any linear combination of the two equations also must work with the same x and y values. So when you subtract one from the other, whatever you are left with must work with the pairs of coordinates as well. As we are left with a straight line equation, this MUST travel through the two points of intersection. As for your second point, I've identified it as EXTENSION as it is beyond what you would be expected to do in the exam, and as you say, is there to spark further interest.

[@sweettoy3824]

guys.... we should've watched this beforehand...

[@abdullahhussain9589]

What?! Still searching KZbin for Maths help?? Are the videos from 2006 really helping ?? 🤬 I hate these types of ads

[@TLMaths]

Damn Study Pug

[@teatime9198]

@@TLMaths Haha yeah, when all the videos you need are from @TLMaths, I cannot thank you enough for the content you've provided! I'll be sure to give you a coffee mate

[@michellesilva7366]

Hi jack could you pls let me know where the -735/121x came from?

[@TLMaths]

From expanding ((5/11)*x-147/22)^2 you get the middle term of 2*(5/11)*x*(-147/22) = -(735/121)*x

[@michellesilva7366]

TLMaths and I have a small question. The lines y=x-5 and y=3x-13 intercects at point S. The point T has a coordinate (-4,2).find the equation of the line that passes through point s and t. Could you pls let me know how to solve this if you don’t mind?

[@TLMaths]

First find where y = x - 5 and y = 3x - 13 intersect: x - 5 = 3x - 13 8 = 2x 4 = x When x = 4, y = 4 - 5 = -1, so S has coordinates (4,-1). T has coordinates (-4,2). The gradient of the line passing through S and T is (-1 - 2)/(4 - -4) = -3/8 So the line passing through S and T is y - 2 = (-3/8)*(x + 4) which is y = (-3/8)*x + 1/2

[@michellesilva7366]

TLMaths thank you so much!

[@beccasouthwick]

how could you approach this if there is an unknown in one of the équations? eg. x^2+y^2-18x+ky+90=0 and x^2+y^2-2x-2y-34=0

[@TLMaths]

x^2 + y^2 - 18x + ky + 90 = 0 (1) x^2 + y^2 - 2x - 2y - 34 = 0 (2) (1)-(2) - 16x + (k+2)y + 124 = 0 www.desmos.com/calculator/vqwo6a2t1w

[@jalajarora2331]

Is this on the Edexcel spec because our teacher has taught us the whole of circles chapter and we have learnt how to determine the intersection points of lines and circles but not circles and circles?

[@dynam1cdrox711]

Yes theyre all the same content and syllabus regardless of exam board. The only difference is you will get different questions.

[@Springswan345]

Hi jack, Is this also for Gce Alevel math 9709?

[@TLMaths]

The Cambridge International A-Level Maths has a different specification. There will be a lot of overlap but some differences.

[@Abdowksnns283]

Plz i wanna a proof of this method, Proof why does subtraction of equations of two circles give a straight line passes through them... If u can give me a certain link 🙏

[@TLMaths]

It think this is the best thing I can find: mathmaine.com/2013/12/26/linear-systems-why-does-linear-combination-work-graphically/

[@Lewis-nb7pn]

Could’ve you made the equations equal and then solved for x?

[@TLMaths]

How did you want to make them equal? Try it and see

[@Lewis-nb7pn]

I’m guessing it’s the same concept

[@ismailrahman2679]

Hi jack do we need to know any extensions include. I think I've asked this before, just wanted to make sure. Thanks.

[@TLMaths]

The extensions are meant to be beyond the scope of the course.

[@ismailrahman2679]

@@TLMaths Thank you sir.

[@lewisanderson5512]

What mode do you use on the calculator?

[@TLMaths]

To solve the quadratic? Go to mode, then scroll down to x y = 0, then polynomial, degree 2, then type in the coefficients. Keep pressing equals and it'll swap through the two solutions, then the coordinates of the turning point.

[@lewisanderson5512]

Okay thank you

[@film.jonathanelia]

what's to 35f menas?

[@TLMaths]

sorry what?

[@mitch6516]

3SF? 3 significant figures

[@theo.anthony]

You forgot the 4 as the coefficient. Look at the two circle equations, then look at 4:57.

[@TLMaths]

I'm substituting into the original equation (x+2)^2+(y-3)^2=121, not the expanded version x^2 + 4x + y^2 - 6y - 108 = 0.

[@beccasouthwick]

on the second equation it doesn’t say 4(x+2)^2 …. it says &(x+2)^2 . If that is what you meant by the coefficient???

[@ColinRichardson]

0:06 Sorry, I've got 6 seconds in, and you already lost me. "These two circles".. WHAT 2 circles? Those are equations.. Why are there squares? Why are the x and y coordinates reversed... you said radius of 10? but the number says 100... WHY?? WHY can't you just write things normally?

[@TLMaths]

(x-a)^2 + (y-b)^2 = r^2 is the equation of a circle centred at (a,b) with radius r. Might want to start with C2-01

[@ColinRichardson]

​@@TLMaths I got there in the end.. the javascript of it I boiled down is much easier to understand than the mathematical interpretation. I eventually even managed to boil it down from 2 seperate points, to a single deltaPoint so it doesn't actually matter what the real coordinates are, just how far apart they are. So the only things I REALLY needed in the end was radius 1, radius 2, x delta, y delta. I can just translate the values (if needed) onto point1 afterwards.