Question

from all the points of the circle x^2+y^2=4
point(x0,y0) is the farthest from the line: x-2y-1=0
so x0+y0=?

Answer 1

from the line, we have y = 1/2x -1 so that the perpendicular line to that line has the form
y=-2x +C

Answer 2

okay..

Answer 3

the line will cut the circle at 2 points and the farthest point on the circle will be the perpendicular line with the given line at the middle point, right?

Answer 4

right!

Answer 5

and every line perpendicular to the arc at the middle point passes through the center, right?

Answer 6

you have the center, you have the middle point, you have the form of the circle, you can find x0, y0, do whatever you want

Answer 7

but how do i know which one to use for what?! :O

Answer 8

the perpendicular line pass through the center is y =-2x (because y =0) (1)
so that , if this line cut the circle, you will have y^2 +x^2 =4 (2)
square both sides of (1) you have y^2 =4x^2, replace to (2) you have 5x^2=4, x =\(\pm\dfrac{2}{\sqrt5}\) , replace back to (1) to find y

Answer 9

another question how do i know if i should use + or - value of x?

Answer 10

when i sum those two..

Answer 11

As I told before, when you get x0, y0, do whatever you want, times them, add them, subtract them, exponent them and whatever....... You can "eat" them too. hihihih

Answer 12

XD
yea but the answer isn't the same :D

Answer 13

sure, because when you eat them, they disappear, hihihiih... Whatsoever, you have the way to find them out. Now is your duty. me done

Answer 14

okay :p

Answer 15

nice :)