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?

Answer 1

Substitute the radius and the point (2, 6 ) into x2 + y2 = r2 and simplify.

Step-by-step explanation:

Since the point (0,4)lies on the circle, the circle's radius is 4.

The equation for a circle that centers at (0,0) is x2 + y2 = r2.

If the point (2,6) lies on the circle the coordinates will satisfy the equation.

Substitute (2,6 ) into the :

22 + (6)2 = 42

4 + 6 ≠ 16

The point is not on the circle.

Answer 2

If the circle is at the origin and (0,4) is a point on the circle then the radius of the circle is:

r^2=0^2+4^2

r^2=16

r=4

so we can check that the other point is four units from the origin and thus also on the circle...

d^2=2^2+6^2

d^2=4+36

d^2=40

since d^2>r^2, (2,6) is outside the circle...