Question

Which point lies inside the circle with equation (x - 2)2 + (y + 3)2 = 4?
0,-3
2,-4
2,0
2,-5

Answer 1

center (h,k) = (2,-3)

Answer 2

radius = 2

Answer 3

2 of the choices lie ON the circle,
1 of the choices is IN the circle
1 of the choices is OUTSIDE the circle

Answer 4

but there is no (2,-3) listed for the answers

Answer 5

that is the center of the circle

Answer 6

you want one that is INSIDE the circle

Answer 7

Addition: If a point \((x_0 ,y_0 ) \) lies inside a circle, then its distance from the centre is less than the radius.\[\sqrt{(x_0 - h)^2 + (y_0 - k)^2} < r\]\[(x_0 - h)^2 + (y _0 - k)^2 < r^2\]

Answer 8

if you say

(x-2)^2 + (y+3)^2 < 4

Answer 9

If you have for a point (x, y) that (x-2)^2 +(y+3)^2 <4, then the point (x, y) is inside.
If you have for a point (x, y) that (x-2)^2 +(y+3)^2 >4 then (x, y) is outside the circle.
If you have for a point (x, y) that (x-2)^2 +(y+3)^2 =4 then the point (x, y) is on the circle.

Answer 10

In other words, all the points satisfying \((x - h)^2 + (y - k)^2 < r^2\) will lie inside the circle.

Answer 11

You would be better off doing a sketch on graph paper and solving geometrically.

Answer 12

right, i did that above there

Answer 13

(2 , -3)