Question

Which of these points lies on a circle centered at A(3, 3) and passing through B(6, 5)?
C(1, 6)
D(6, 0)
E (0, 3)
F(3, -1)
G(3, 6)

Answer 1

I think the easiest way to approach this, would be firstly to apply the distance formula between A and B (since B lies on the circle and is not the centre, it must lie on the circumference) so by finding this distance, we can determine the radius

Answer 2

do you remember the distance formula?

Answer 3

\[2pr ^{2}\]

Answer 4

not quite, thats the circumference formula, we want the distance between two points

Answer 5

so the equation you want to use is \[d = \sqrt{(y - y1)^2 + (x - x1)^2}\]

Answer 6

oh yea

Answer 7

yup, so apply that and tell me what you get for the distance

Answer 8

3.6

Answer 9

@FireKat97

Answer 10

yup, thats correct! but as a general rule, when we get square roots and stuff, you're better off keeping your answer in exact form, so just stick with √13

Answer 11

btw do you remember what the general equation of a circle is?

Answer 12

not really

Answer 13

okay so the general equation of a circle is-
(x - {x coordinate of centre})^2 + (y - {y coordinate of centre})^2 = radius^2

Answer 14

and we have been given the centre, and had recently worked out the radius, so try subbing in the info we now have, and show me what you get

Answer 15

2.32?

Answer 16

umm, not exactly, so we sub in the stuff we now know to get,
(x - 3)^2 + (y - 3)^2 = (√13)^2
so (x - 3)^2 + (y - 3)^2 = 13
do you follow?

Answer 17

yes

Answer 18

okay, so now we can try subbing the points given as options into our equation, to see which coordinates satisfy it.

Answer 19

(1,6)

Answer 20

Yup! Thats correct!

Answer 21

thankyou!

Answer 22

no problem :)