Question

Fool's problem of the day,

If \( 4x^2+12xy+by^2+6x+2fy-4=0 \) represents a pair of parallel lines, can you find the distance between them?

Genre: Standard analytic geometry problem (Pair of straight lines)
Rating: Easy (If you know how to do it)

Answer 1

only fool and ishaan can understand one another tsk tsk @_@ hahaha

Answer 2

Hmm
\[\frac{\sqrt{\frac{4f^2}{b^2} + \frac{16}{b}}}{1 + \frac{9}{f^2}}\]

Answer 3

Not accepted, from you Ishaan ;) ... are you sure we can't find the value of \( b \) and \( f \)? ;)

Answer 4

Okay I will leave now, keep trying guys, I will post the solution the next time I come online :)

Answer 5

B = 9, F = 9/2 ?

Answer 6

Is that right?

Answer 7

Distance = 11/9?
I am not sure though, I could be wrong, I had to derive the whole thing and made it complex than usual :/

Answer 8

Took me 20 minutes :/ nooooooo, my skills in Geometry are deteriorating :(

Answer 9

I did something wrong... Let me check it

Answer 10

\[\frac{\sqrt{\frac{4f^2}{b^2} + \frac{16}{b}}}{\sqrt {1 + \frac{9}{f^2}}}\]Distance = \(\frac{5}{3\sqrt{11}}\)
\[\Huge \color{gray}{\text{_____________________________________}}\]

Disgraceful :/

Answer 11

Just \(\frac{5}{\sqrt{11}}\), no three

Answer 12

I got \( \large \frac 5 {\sqrt{13}} \)

Answer 13

You got the correct value of f and g, :)

Answer 14

Yeah, 4+9 = 13, not 11.