Find the induvidual equations of the lines represented by 3x^2+8xy-3y^2+2x-4y-1=0

Question

tkhunny · Answer

An easy way might just be to find two points on each line.

Try x = 0 and see what y-values are produced.
Try x = 1 and see what y-values are produced.

You might be almost done, after that.

anonymous · Answer

@tkhunny  how does that help ?

tkhunny · Answer

How do two points help you determine a line?

x = 0 leads to y = 1/4 -- There is a point that must be on both lines.

You can try y = 0 leading to x = 1/2, but now, with only two points, we are going to get only one line.

Forget we did y = 0.  Try x = 1 and see what happens.

anonymous · Answer

wouldnt you get 
$$-3y^2-4y-1=0$$

anonymous · Answer

@tkhunny  with the roots -1 and -1/3??

anonymous · Answer

@tkhunny aha
I see your approach. good

anonymous · Answer

so, the y-intercepts of the two lines are:
-1 
and -1/3

anonymous · Answer

@Yahoo! do you follow?

anonymous · Answer

Yeah..

anonymous · Answer

there you go,
now all you need is the slopes

anonymous · Answer

hint..
since the co-efficients of x^2 and y^2 are same, I think the two lines are perpendicular!

anonymous · Answer

Nice tkhunny :)

tkhunny · Answer

If it's easy, it's easy.  No sense beating it to death.  :-)  Of course, we DID have to know the conic was degenerate, first.

shubhamsrg · Answer

@tkhunny can;'t it represent 2 points from 2 different lines ?

shubhamsrg · Answer

I;d treat it as a quadratic eqn in y and solve for y

tkhunny · Answer

@shubhamsrg That is a good point, and maybe I didn't stress that enough.  I tried to pick the easiest possible values.  In this case, it was clear enough that either x = 0 or y = 0 would result in a point on both lines.