Question

Which point lies inside the circle with equation (x-2)^2+(y+3)^2=4

Answer 1

2,-3

Answer 2

Thats what I thought, but I only have these answers to chose from.
(2, -5)
(2, -4)
(0, -3)
(2, 0)

Answer 3

They're not looking for a center i think, just whats within the circle.

Answer 4

its (2,0)

Answer 5

the equation suggests that it has the centre (2,-3) and radius 2.........

so u can try imagining for the circle and find which point lies inside and which outside.

Answer 6

Or you can use another method.

Answer 7

which is pretty simple

Answer 8

0,-3 would be the answer

Answer 9

0, -3 is on it the edge. take a look

Answer 10

let me give u the best method that i know

Answer 11

Is the image i posted above correct or is the radius 4, thus the diameter would be 8 instead of 4 like in the pic

Answer 12

As when you substitute 0,-3 you will get rhs= lhs

Answer 13

seems to be (2,-5) from graph

Answer 14

@nishika17

wrong

this means that it lies on the circle.

Answer 15

let f(x,y) = (x-2)^2+(y+3)^2-4
now plug in the given points in f(x,y)
if for the given points,
f(x,y) <0 -->point is inside circle
f(x,y) =0 -->point is on the circle
f(x,y) >0 -->point is outside the circle
you may try now

alternative method :
you know center and radius here
you may calculate distances of given points and center
if its>radius -->outside circle
=radius -->on circle
<radius -->inside circle

Answer 16

(2, 0)

Answer 17

just take any point about which u r sure that it lies inside the circle........

then
check whether on putting the values in eq. it gives lhs>rhs or lhs<rhs........

now try putting the values from the options ...

one which gives the same inequality as u got above will be ur answer

or u can even use the distance formula to find the distance of the points given in the options from the centre of the circle.

if its > radius============= lies outside the circle

if its <radius ============= lies inside the circle.

Answer 18

this is what @shubhamsrg
has done..........

Answer 19

Both (0,-3) and (2,-5) are giving radius as 2 and for both lhs= rhs

Answer 20

So, @nishika17 they cannot be the correct answers./........ because this means that they lie on the circumference of the circle......