Given distance 2 from origin to line 5x+12y-a=0 , calculate a?
You need to use the following formula that helps you to evaluate the distance from a point `A(x_A,y_A)` to a line `ax + by + c = 0` , such that:
`d = |ax_A + by_A + c|/(sqrt(a^2 + b^2))`
The problem provides the distance `d = 2` from origin point `(0,0)` , to the line `5x + 12y - a = 0` , such that:
`2 = |5*0 + 12*0 - a|/(sqrt(5^2 + 12^2))`
`2 = |-a|/sqrt(25+144) => 2 = |a|/sqrt169 => |a| = 2*13 = 26`
Using the absolute value definition yields:
`|x| = t => x = +-t`
By definition, yields:
`|a| = 26 => a = +-26`
Hence, evaluating the constant term `a` , under the given conditions, yields `a = +-26` .