Question

how can you find two points on the circle if you are given the center and radius? well.. it says an equation of a circle is given. a. determine its center. b. determine its radius c. find two points on the circle. (x-4)^2 + (y-2)^2 = 196 so far I have.. a.(4,2) b. r=14

Answer 1

if you want to test whether of not a point (x,y) is on a circle, and you have the equation of the circle, you need to plug the values of x and y into the equation, and see if the point is a solution to the equation. For example, (0,0) is not on the circle since:
\[(0-4)^2+(0-2)^2\ne 196\]

Answer 2

yes--the only problem I am having is out to find the right coordinates that work for the equation.. I forgot what to do

Answer 3

Worst case scenario, you could try guessing some points, plugging them in and seeing how close you can get to 196. Or try to draw a neat picture, and guess by looking at the picture. You know the center is (4,2), and the radius is 14. Getting that info is half the battle.

Answer 4

Yeah.. I know I could draw all of them out.. but I do know that there has to be a faster way to solve it.. I just forgot what it was....

Answer 5

if you know the center (h, k) and radius (r) of the circle, then to get any point on the circle choose any x-value in this range [h-r, h+r], plug that x value into the equation of that circle and solve for y...

Answer 6

so would I do -4 + -2?

Answer 7

or i mean 4 +2

Answer 8

in your problem, Center is (4, 2) with radius 14.
choose any value in [4-14, 4+14] or [-10, 18]. choose...

Answer 9

let's choose an "easy" one. let's choose x=0..

Answer 10

or would the radius just be 196 because I took the sq rt of 196 to get 14

Answer 11

radius is 14. that 196 is from the equation of your circle (it determines your radius)

Answer 12

ohh ok

Answer 13

can you solve this equation to get the y-coordinate of the point that's on the circle?