Question

Find the distance between 2x+y+4=0 and 2x+y+8=0.

(a) \(\frac{4}{\sqrt{5}}\)

(b) \(\frac{3}{\sqrt{5}}\)

(c) \(\frac{9}{\sqrt{5}}\)

(d) \(\frac{3}{\sqrt{2}}\)

I had been asked this question in final exam.

My question is from Distance of a Point from a Line in chapter Straight Lines of Mathematics – Class 11

Answer 1

Right option is (a) \(\frac{4}{\sqrt{5}}\)

For explanation: Distance between parallel lines ax +by +c1=0 and ax+by+c2=0 is \(|\frac{c1-c2}{\sqrt{a^2+b^2}}|\).

So, distance 2x + y+4=0 and 2x+y+8=0 is \(|\frac{8-4}{\sqrt{2^2+1^2}}|=\frac{4}{\sqrt{5}}\).