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if `P` is the length of perpendicular from origin to the line `x/a+y/b=1` then prove that `1/(a^2)+1/(b^2)=1/(p^2)`

Text Solution

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The given line is
`bx+ay-ab = 0 " "(1)`
It is given that p is the length of the perpendicular from the origin to (I), that is,
`p = (|b(0) + a(0) -ab|)/(sqrt(b^(2) + a^(2)))`
`=(ab)/(sqrt(a^(2) + b^(2)))`
` " or " p^(2) = (a^(2)b^(2))/(a^(2) + b^(2))`
` " or " (1)/(p^(2)) = (a^(2)+ b^(2))/(a^(2)b^(2)) = (1)/(a^(2)) + (1)/(b^(2))`
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