• # question_answer The shortest distance from the line $3x+4y=25$ to the circle ${{x}^{2}}+{{y}^{2}}=6x-8y$ is equal to A) 7/5        B) 9/5 C) 11/5                              D) 32/5

[a]  Equation of circle ${{x}^{2}}+{{y}^{2}}-6x+8y=0$ ${{(x-3)}^{2}}+{{(y+4)}^{2}}=25$ Centre $(3,-\,4),$radius = 5 Distance from $(3,-\,4)$to the line $3x+4y-25=0$is $d=\left| \frac{9-16-25}{5} \right|=\frac{32}{5}$ Shortest distance $=d-r=\frac{32}{5}-5=\frac{7}{5}$