Question

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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.

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Answer 1

Concept : use intercept form of line : x/a + y/b = 1 and then find perpendicular distance of point from line .

equation of line in intercept form is

x/a + y/b = 1

x/a + y/b - 1 = 0 .

now, use formula

distance of point (x1, y1) from line : ax + by + c =0 is |ax1 + by1 + c|/√(a²+b²)

so, it's distance from origin is

P = | 0 + 0 -1|/√(1/a² + 1/b²)

P = 1/√(1/a² + 1/b²)

1/P = √(1/a² + 1/b²)

take square both sides,

1/P² = 1/a² + 1/b²

hence proved.

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Answer 2

Answer:

☞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 1p2=1a2+1b2.