SOLUTION: if p is the length if the perpendicular from the origin to the line x/a + y/b = 1, prove that 1/p� = 1/a� + 1/b�. I assume I'll have to use the perpendicular distance formula so

Question 698546: if p is the length if the perpendicular from the origin to the line x/a + y/b = 1, prove that 1/p� = 1/a� + 1/b�.
I assume I'll have to use the perpendicular distance formula somehow, but I don't really know what to do ...
Answer by Edwin McCravy(20062) (Show Source): You can put this solution on YOUR website!

The formula for the perpendicular distance from (x₁,y₁)
to the line whose equation is Ax+By+C=0 is

d = 

The line has the equation

 +  = 1  

[Don't get capital A and B confused with little letters a and b]

Clear of fractions by multiplying by LCD = ab:

     bx + ay = ab

Get 0 on the right

bx + ay - ab = 0

For (x₁,y₁) = (0,0)

Substitute in

d = 

with d = p, A = b, B = a, C = -ab, (x₁,y₁) = (0,0)

p = 

p = 

Square both sides

p� = 

Take the reciprocal of both sides:

 = 

Make two fractions on the right:

 = 

 = 

 = 

Edwin

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