Question

Find the equation of the circle passing through the points (-4,-2) and (2,0) and having its center on the line 5x-2y=19.

I need two forms of answer...
general and standard...
its okay if you give me a general equation
b'coz I knew already how to convert general equation to standard.

Answer 1

how is your work finding last digit of pi ?

Answer 2

wow... until now you still remembered it?

Answer 3

wow indeed lol

Answer 4

the eq of the circle will b (x-x1)^2+(y-y1)^2=r^2
since the points given r in the circle they prove the eq of the circle and since the center is in the line 5x-2y=19 then its coordinates prove the eq of the circle... so we can form the system

(-4-x1)^2+(-2-x1)=r^2
(2-x1)^2+(0-y1)^2=r^2
5x1-2y1=19

Answer 5

what about the general eq.

Answer 6

hmm....isn't this the general eq?

Answer 7

the general eq. is this x^2+y^2+Dx+Ey+F=0

Answer 8

well after u've found the eq (x-x1)^2+(y-y1)^2=r^2 all u have to do is transform it x^2-2xx1-x1^2...etc...and this is how i get it

Answer 9

the standard eq. is this\[(x+h)^{2}+(y+k)^{2}=0\]

Answer 10

I think you've used the calculus in solving this problem.

Answer 11

I think that's conic

Answer 12

tht's conic....

Answer 13

http://www.wolframalpha.com/input/?i=solve+the+system+%28-4-x1%29^2%2B%28-2-x1%29%3Dr^2%3B+++%282-x1%29^2%2B%280-y1%29^2%3Dr^2%3B++5x1-2y1%3D19 this is wht Wolfram says

Answer 14

That's a sort of "help" formula based on completing the square..

Answer 15

oh my brain malfunctioned that is the general equation sorry

Answer 16

Your brain didn't malfunction, it isn't standard, just meant to help the student...

Answer 17

Thanks estudier : )

Answer 18

I don't like questions like this ...

Answer 19

I still think the simplest method for solving this sort of thing is to translate to the origin but I suppose that might be going beyond....

Answer 20

eaularch just use the formulas distance one then convert it into any equation you like

Answer 21

what is that is that really way beyond translate

Answer 22

okay you're saying make the center 0,0 right?

Answer 23

Everything is just much easier to calculate at (0,0)..

Answer 24

oh okay

Answer 25

Then when u got it, translate it back..

Answer 26

Anyway, I am just trying to think of a simple way to explain...(without translation).

Answer 27

yeah thanks I will try this tonight thanks estudier these type of questions are asked a lot in india especially in IIT,AIEEE exams (for entering top colleges in India) I will try this.
Thanks

I gotta go now bye and thanks estudier

Answer 28

Ciao!

Answer 29

Estudier it is easier if the center was at (0;0) but it is not ;/

Answer 30

It's just a translation, quite simple.