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Prove that the lengths of the perpendicu...

Prove that the lengths of the perpendiculars from the points `(m^2,2m),(m m^(prime),m+m^(prime)),` and `(m^('2),2m^(prime))` to the line `x+y+1=0` are in GP.

Text Solution

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`p_(1) = (m^(2) + 2m+1)/(sqrt(2)) = ((m+1)^(2))/(sqrt(2))`
`p_(2) = (|mm' +m+m'+1|)/(sqrt(2)) = (|(m'+1)(m+1)|)/(sqrt(2))`
`p_(3) = ((m')^(2) +2m'+1)/(sqrt(2)) = ((m'+1)^(2))/(sqrt(2))`
`"Clearly", p_(1), p_(2) " and "p_(3) " are in GP."`
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