A circle that is centered at the origin contains the point (0,4). How can you prove or disprove that the point (2,
6
) also lies on the circle? Does the point (2,
6
) lie on the circle?

Question

A circle that is centered at the origin contains the point (0,4). How can you prove or disprove that the point (2, 
	6
) also lies on the circle? Does the point (2, 
	6
) lie on the circle?

amorfide · Answer

you know the centre (0,0)
and you know that (0,4) is a point on the circle

figure out the radius by doing the formula for length of a line going through two points
$$d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$$

then you write your equation for a circle
$$(x+0)^{2}+(y+0)^{2}=r^{2}$$
not sure how to finish this

@rvc

amorfide · Answer

oh I know

amorfide · Answer

you would use the same distance formula for the point given and the origin
if you get the radius to be the answer then it lays on the circle

rvc · Answer

yep!
correct :)

anonymous · Answer

oh wow really? Its been a long day and home work is getting rough, thank you

amorfide · Answer

hope it is clear, feel free to ask questions if not

rvc · Answer

All the best !