if distance between the pair of parallel lines `x^2+2xy+y^2-8ax+8ay-9a^2=0` is `25sqrt2` then `a/5' is equal to

Explanation

In the given equation,

`a' = 1,b = 1, c = -9a^2, h = 1, g = -4a, f = 4a`

Distance between pair of parallel lines `= 2 sqrt((g^2-a'c)/(a'(a'+b))`

`=>2 sqrt((16a^2+9a^2)/(1(1+1))) = 25sqrt2`

`=>+-5sqrt2a = 25sqrt2`

`=> a= +-5`

`:. a/5 = +-1.`