Question

Determine o valor de K , de modo que a distancia do ponto p(2,1) à reta (r) 3x-4y+k=0seja igual a 4 

Answer 1

$\begin{cases} & \text{ } A= 3 \\ & \text{ } B= -4 \\ & \text{ } C= k \\ & \text{ } Xo=2 \\ & \text{ } Yo= 1 \\ & \text{ } d= 4 \\ \end{cases}\\\\ d = \frac{| AXo + BYo + C|}{ \sqrt{A^{2} + B^{2}} } \\\\ 4 = \frac{| 3*2 + 4*1 + k|}{ \sqrt{3^{2} + (-4)^{2}} } \\\\ 4 = \frac{| 10 + k|}{ \sqrt{25} } \\\\ 4 = \frac{10 + k}{5} \\\\ 10 + k = 20\\\\\boxed{k = 10}$