Find the shortest distance from the origin to the link 3x+2y=4....
is there an easy method to do this?
THANKS
$\displaystyle x^2 + y^2 = 25 $ is a circle of radius $\displaystyle 5 $.
$\displaystyle 3x-4y = 0 $ is the line $\displaystyle y = \frac{3}{4}x $.
So to do it graphically, find where the line and circle intersect.
We know $\displaystyle y = \frac{3}{4}x $.
Then $\displaystyle x^2 + \frac{9}{16}x^2 = 25 $ or $\displaystyle \frac{13}{16}x^2 = 25 $.
So $\displaystyle x \approx 5.54, \ y \approx 4.155 $