may be its easy...

AIEEE 2015 Tutorials › Co-ordinate Geometry questions › may be its easy...

Two straight lines cut the axis of x at distances a and -a and the axis of y at distances b and bÂ° respectively; find the coordinates of their point of intersection.

Ans:- {a(b-bÂ°)(b+bÂ°), 2bbÂ°(b+bÂ°)}

From: S.L.Loney :)

#Mathematics #Co-ordinate Geometry

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2 Answers

kaymant ·Oct 21 '09 at 15:22

The first line is
$ a x + b y = 1$
And the second one is
$ - a x + b ' y = 1$
(I am using b' instead of bÂ°)
Solve them simultaneously: Add them to get the y coordinate as
$y\left(\dfrac{1}{b}+\dfrac{1}{b'}\right)=2\quad \Rightarrow \ y =\dfrac{2bb'}{b+b'}$
And the x coordinate as
$x = a (1 - b y ) = a (1 - b + b ' 2 b ' ) = b + b ' a (b - b ' ) $