Two parallel lines lying in the same quadrant make intercepts a and b on x and y axes, respectively, between them. The distance between the lines is (a) `(ab)/sqrt(a^2+b^2)` (b) `sqrt(a^2+b^2)` (c) `1/sqrt(a^2+b^2)` (d) `1/a^2+1/b^2`

Options

A. `sqrt(a^(2) + b^(2))`
B. `(ab)/(sqrt(a^(2) + b^(2)))`
C. `(1)/(sqrt(a^(2) + b^(2)))`
D. `(1)/(a^(2))+(1)/(b^(2))`

Answer

B

Explanation

From the figure
`"cos" theta = (h)/(a) " and sin"theta= (h)/(b)`
Squaring these and then adding, we get
`1 = (h^(2))/(a^(2))+ (h^(2))/(b^(2))`
`therefore h = (ab)/(sqrt(a^(2)+ b^(2)))`