Question

Find six distinct points on the circle with center (2,3) and radius 5

Answer 1

equation of a circle with center (x0, y0) and radius R is:
(x - x0)² + (y - y0)² = R²

Answer 2

if we plug this values, we get:
(x - 2)² + (y - 3)² = 25

Answer 3

now make combinations of x and y so that this equation is satisfied

Answer 4

plz make 1 combination so i can make another

Answer 5

is there any method for making combination

Answer 6

if i set x = 2, then:
(y-3)² = 25
y-3 = 5
y = 8, so point (2,8) is in the circle

Answer 7

we have another one, since \[\sqrt{25} = \pm 5\]

Answer 8

so
y-3 = -5
y = -2, so point (2,-2) is also a point in the circle

Answer 9

now, set y = 3 and find more two values for x, after that we already have four points

Answer 10

we can put any value of x and find y ? or is there any rule for assuming the value of x ?

Answer 11

no, you can't

Answer 12

we have a range of possible values for x and y

Answer 13

how i know what are these range

Answer 14

the center of the circle is (2,3) and radius 5, so x is inside range x = [2-5,2+5] and
y = [3-5,3+5]

Answer 15

oh i see thanks a lot thank u so much

Answer 16

but you must choose one of these point, plug in the equation to find the assotiated values

Answer 17

because this range that i gave you, is a ractangle, not a circle, what defines a circle it's equation

Answer 18

the range which u gave me is correct ? i can chose that one ?