Asked by Prakash
Which formula is used to find the length of perpendicular from origin to the line x/a + y/b = 1?
Answers
Answered by
oobleck
The line x/a + y/b = 1 can be written as
bx + ay = ab
This line has slope -b/a, so the perpendicular line has equation
y = a/b x
The lines intersect at
x = ab^2/(a^2+b^2)
y = a^2b/(a^2+b^2)
so the distance from (0,0) to the intersection is
d = |ab|/√(a^2+b^2)
bx + ay = ab
This line has slope -b/a, so the perpendicular line has equation
y = a/b x
The lines intersect at
x = ab^2/(a^2+b^2)
y = a^2b/(a^2+b^2)
so the distance from (0,0) to the intersection is
d = |ab|/√(a^2+b^2)
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