# 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?

$a = 1 \mathmr{and} a = - \frac{37}{3}$
We know perpendicular distance (D) from a point $\left(m , n\right)$ to a line of equation Ax+By+C=0 ; D= |Am+Bn+C|/sqrt(A^2+B^2)
So here ,$4 = | 3 a + 4 \cdot 3 + 5 \frac{|}{\sqrt{{3}^{2} + {4}^{2}}} \mathmr{and} | 3 a + 17 | = 20 \therefore 3 a + 17 = 20 \mathmr{and} a = 1$ Also $3 a + 17 = - 20 \mathmr{and} a = - \frac{37}{3} \therefore$
$a = 1 \mathmr{and} a = - \frac{37}{3}$[Ans]