Two straight lines cut the axis of x at distances a and -a and the axis of y at distances b and b° respectively; find the coordinates of their point of intersection.
Ans:- {a(b-b°)(b+b°), 2bb°(b+b°)}
From: S.L.Loney :)
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2 Answers
66The first line is
\dfrac{x}{a}+\dfrac{y}{b}=1
And the second one is
\dfrac{x}{-a}+\dfrac{y}{b'}=1
(I am using b' instead of b°)
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\left(1-\dfrac{y}{b}\right)=a\left(1-\dfrac{2b'}{b+b'}\right)=\dfrac{a(b-b')}{b+b'}
