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C1 question!!

Prove that the circle: x^2 + y^2 -2x - 6y = 15 cuts the circle
x^2 + y^2 - 16x - 4y = -59 in two distinct places and find the equation of the common cord??


Well I tried to solve simultaneously, to get 14x - 2y = 74. Is that the equation of the common chord? Also how do you find the other part to the question??

Many thanks.
(edited 12 years ago)
Reply 1
Avatar for TenOfThem
TenOfThem
18
Do you mean 14x or was one of the original circles typed incorrectly

Whichever ... rearrange to get y= and then sub into one of the circle equations
Solve your linear equation simultaneously with that of one of the circles.
Reply 3
Avatar for master y
master y
OP
12
yup, then I get 5x^2 - 162x +1591..... then i tried to solve quadratically, and it did not work :frown:
Your linear equation is wrong by the way.
Reply 5
Avatar for master y
master y
OP
12
Original post by TenOfThem
Do you mean 14x or was one of the original circles typed incorrectly

Whichever ... rearrange to get y= and then sub into one of the circle equations


ooops, yup it is 14, well spotted!! That means I've done it wrong... let me try again!
Reply 6
Avatar for master y
master y
OP
12
Gah it STILL doesnt work... I don't know what i am doing wrong!!
Original post by TenOfThem
...was one of the original circles typed incorrectly


Can't be this or they wouldn't intersect.
Original post by master y
Gah it STILL doesnt work... I don't know what i am doing wrong!!


Show your working as it does work perfectly well.
Reply 9
Avatar for master y
master y
OP
12
Original post by Mr M
Show your working as it does work perfectly well.


ok.

so sub in y= 7x - 37
x^2 + (7x - 37)^2 - 2x - 6(7x - 37) = 15
--> 25x^2 - 237x +788.... (which solves to no real roots!) :L
Reply 10
Avatar for master y
master y
OP
12
bump
Reply 11
Avatar for master y
master y
OP
12
Original post by Mr M
.


Dude, please could you tell me how you got to the solution?? It would be really helpful, Thanks!
(edited 12 years ago)
Original post by master y
ok.

so sub in y= 7x - 37
x^2 + (7x - 37)^2 - 2x - 6(7x - 37) = 15
--> 25x^2 - 237x +788.... (which solves to no real roots!) :L


The -237 is wrong.
Reply 13
Avatar for Paul-Ings
Paul-Ings
6
which exam board do you do?
Reply 14
Avatar for master y
master y
OP
12
Original post by Paul-Ings
which exam board do you do?


ocr...why?
Reply 15
Avatar for Paul-Ings
Paul-Ings
6
Original post by master y

Original post by master y
ocr...why?


ah right sorry, was just curious because everyone has been asking about chords and I had no idea about chords in C1 and didn't even know that they feautured, because I do edexcel... I was just curious to see if I've missed a section
(edited 12 years ago)
Original post by Paul-Ings
ah right sorry, was just curious because everyone has been asking about chords and I had no idea about chords in C1 and didn't even know that they feautured, because I do edexcel... I was just curious to see if I've missed a section


I would have hoped you would remember the word chord from GCSE - you would have certainly met it when you studied circle theorems.
Reply 17
Avatar for master y
master y
OP
12
Original post by Paul-Ings
ah right sorry, was just curious because everyone has been asking about chords and I had no idea about chords in C1 and didn't even know that they feautured, because I do edexcel... I was just curious to see if I've missed a section


Lol, there's no need to be sorry. Im not sure whether chords are in the OCR syllabus as well as I hav not met any of the questions like this in past papers. I'm just preparing for the worst!

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