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Let d1 and d2 be the lengths of the pe...

Let `d_1` and `d_2` be the lengths of the perpendiculars drawn from any point of the line `7x-9y+10= 0` upon the lines `3x+ 4y =5` and `12x+ 5y= 7` respectively. Then `(A) d_1> d_2 (B) d_1=d_2 (C) d_1< d_2 (D) d_1= 2d_2`

Text Solution

Verified by Experts

`7h-9y+10=0`
`9y=7h+10`
`y=(7h+10)/9`
`d_1=|(3h+4((7h+10)/9)-5)/sqrt(9+16)|`
`d_1=|(27h+28h+40-45)/45|`
`d_1=|(55h-5)/45|`
`d_1=|(11h-1)/9|`
`d_2=|(12h+5((7h+10)/9)-7)/sqrt(140+25)|`
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