Question

If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that: 1/p² = 1/a² + 1/b²

Answer 1

Equation of line where intercept on the axes are a and b is x/a + y/b =1

Distance from origin (0,0) to the line x/a +y/b =1 in p

So, distance d=p & x₁ = 0 and y₁ = 0

Putting values

∴ Perpendicular distance

Squaring both sides, we get

Hence proved