Consider a line $L$ of equation $ 3x + 4y – 25 = 0 $ and a real circle $C$ of real center of equation $ x^2 + y^2 -6x +8y =0 $
I need to find the shortest distance from the line $L$ to the circle $C$.
How do I find that?
I am new to coordinate geometry of circles and line.
And I noted the slope of $L$ to be $\frac{-A}{B} = \frac{-3}{4} $ which means the line is inclined to $ -37° $ with $+x axis$ And circle centered at $ (3,-4) $ and of radius $5$ units.
By diagram, its difficult to figure out. Can we figure out easily by diagram or there is an algebraic way which is good for this?
Best Answer
Note that the shortest distance between a line and a circle will be the perpendicular distance of the line from the centre of the circle, minus the radius.
The circle can be written as $C=(x-3)^2+(y+4)^2=25=5^2$. So, $?$