Question

Which of the following points lies on the circle whose center is at the origin and whose radius is 10?
(-6, 4)
(square root of 10, square root of 10)
(6, -8)

Answer 1

The equation of the circle whose center is at the origin and whose radius is 10 is:
\[x^2+y^2=10^2\]
\[x^2+y^2=100\]
So, you just have to replace the values of x and y with the abscissa and ordinate of each given point, and see which one gives a correct identity.

Answer 2

so the second one?

Answer 3

Let's check... the point in this case is
\[(\sqrt{10},\sqrt{10})\]
Let's replace x=square root of 10 and y=square root of 10 in the equation of the circle:
\[x^2+y^2=100\]
\[\sqrt{10}^2+\sqrt{10}^2=100\]
\[10+10=100\]
\[20=100\]
So, the second one gives a wrong result.

Answer 4

The right answer is the third point (6,-8), because
\[6^2+(-8)^2=100\]
\[36+64=100\]
\[100=100\]
100=100 is a true identity. Therefore, the third point is the one we're looking for.