Two lines x+2y+3=0 and 2x+3y+4=0 are conjugate with respect to the circle
a)$x^2+y^2=9$
b)$3x^2+3y^2=2$
c)$x^2+y^2=3$
d)$2x^2+2y^2=3$

Actually, I even don't know what conjugate means in this question..

Question

Two lines x+2y+3=0 and 2x+3y+4=0 are conjugate with respect to the circle
a)$x^2+y^2=9$
b)$3x^2+3y^2=2$
c)$x^2+y^2=3$
d)$2x^2+2y^2=3$

Actually, I even don't know what conjugate means in this question..

anonymous · Answer

me too ;) let me search

anonymous · Answer

If each line passes through the pole of the other......

ujjwal · Answer

^^ I don't get it. What does pole refer to?

anonymous · Answer

http://en.wikipedia.org/wiki/Pole_and_polar

apoorvk · Answer

Umm, I had explained pole and polar to someone sometime back, should I post a link to that here?

ujjwal · Answer

yeah @apoorvk

apoorvk · Answer

http://openstudy.com/users/aravindg#/updates/4fc99695e4b0c6963ad3e8a1

anonymous · Answer

i dont know that myself but this may help http://www.math.uoc.gr/~pamfilos/eGallery/problems/Conjugacy.html

ujjwal · Answer

I guess, i understand the pole and polar thing a bit. And now, how am i supposed to solve this question?

experimentx · Answer

https://www.google.com/webhp?rlz=1C1ASUT_enNP447NP447&sourceid=chrome-instant&ie=UTF-8&ion=1#hl=en&rlz=1C1ASUT_enNP447NP447&output=search&sclient=psy-ab&q=conjugate%20line%20wrt%20circle&oq=&gs_l=&pbx=1&fp=183b0c2b7c00e0d7&ion=1&bav=on.2,or.r_gc.r_pw.r_cp.r_qf.,cf.osb&biw=1366&bih=667 seems like a pdf file .. i hate to download.

ujjwal · Answer

It says:
Two lines L1 = 0, L2 = 0 are said to be conjugate with respect to the circle S = 0 if the pole of L1 = 
0 lies on L2 = 0.

Now what am i supposed to do?

anonymous · Answer

i can tell u the construction part which defines pole-polar but, as i said, in hyperbolic geometry i'm not at the formula and calculation part yet..

as far as i remember a pole is a point outside the circle(can be inside but its trouble!) and its polar is the line formed by joining the two points at which its tangent meet.
|dw:1342116321944:dw| A is polar of a here

anonymous · Answer

sry A is pole and a is polar

anonymous · Answer

using coordinate geometry it may be done but the calculation i can think of is going to be really lengthy...

ujjwal · Answer

So, I have line 1 and 2 and i am supposed to find the equation of circle from the list of options..|dw:1342118162351:dw| So, the radius of circle would be equal to the perpendicular distance from center of circle to those lines.. I guess I am getting closer to solution!