Question

The length of the perpendicular drawn from the point (a,3) on the line `3x+4y+5=0` is 4, how do you find the value of a?

Answer 1

`a=1 or a=-37/3`

Explanation:

We know perpendicular distance (D) from a point `(m,n)` to a line of equation `Ax+By+C=0 ; D= |Am+Bn+C|/sqrt(A^2+B^2)`
So here ,`4= |3a+4*3+5|/sqrt(3^2+4^2) or |3a+17|=20 :. 3a+17=20 or a=1` Also `3a+17=-20 or a=-37/3 :.`
`a=1 or a=-37/3`[Ans]