Question

a line passes through the point P (2,3) and makes an angle \[\theta\] with positive direction of x - axis. If it meets the lines represented by \[x^2 - 2xy - y^2 = 0\] at the points A and B. If PA.PB = 17, then find the value of \[\frac{10}{\pi} * \theta\]

Answer 1

@eliassaab

Answer 2

@mukushla
@waterineyes

Answer 3

@apoorvk ?

Answer 4

@vamgadu

Answer 5

can someone help me

Answer 6

its urgent for me.......

Answer 7

@mathslover

Answer 8

\[\left(x-y\right)^2 + \left(\sqrt2y\right)^2=0\]

Answer 9

negative sign in between not positive.

Answer 10

ok

Answer 11

Equation of line must be \(y = mx + 3 -2m\) where \(m=\tan \theta\).

Answer 12

I am sorry I made a foolish mistake in representation both the lines are supposed to have positive slope, I hope you can correct it yourself.

Answer 13

Ok then what do I have to do..............

Answer 14

Point A could be represented as. (2 + PAcos theta, 3 + PA sin theta).

Point B, (2 + PB cos theta, 3 + PB sin theta).

Point A and B must be lie on the line y=mx+3−2m

Answer 15

Also, PA.PB = 17

Answer 16

yes

Answer 17

Now solve it yourself. I have give you enough hints.

Answer 18

given*

Answer 19

So I can apply distance formula

Answer 20

on PA and PB

and then equate

(PA.PB)^2 = 17^2

Answer 21

Why would you apply distance formula? PA and PB are already distances.

Answer 22

No I mean

distance between P and A = PA
distance between P and B = PB

Answer 23

It won't work.

Answer 24

y ?

then what should I do........

Answer 25

@amistre64
@eliassaab
@UnkleRhaukus
@mukushla


someone please help me................

Answer 26

@experimentX

Answer 27

what bit are you up to?

Answer 28

@UnkleRhaukus
I tried finding the value of PA and PB using distance formula and then equating PA.PB = 17 but that didn't want...........

Answer 29

you do have a drawing ?

Answer 30

x^2 -2xy -y^2=0
on solving treating it as quad eqn in x,
2 lines are :
x = y (1+ sqrt(2)) and x= y(1- sqrt(2))
our line is
y= (tan@) x +c
it passes through (2,3) => c=3-2tan@
=>eqn is
y=xtan@ + 3-2tan@
A = intersection of y=xtan@ + 3-2tan@ and x = y (1+ sqrt(2))
solve for x and y
similarly find B
then PA and PB
=>find tan@ or @
you have the ans then

my method seems very long and monotonous..hmm..

Answer 31

@shubhamsrg

thanks a lot for ur help

I did find my answer using the same method but couldn't find an easier one.........

Can u suggest an easier method ?