Question

The center of a circle is at (0,0) and its radius is 5. Does the point (5,-2) lie on the circle?

Answer 1

No

Explanation:

A circle with center `c` and radius `r` is the locus (collection) of points which are distance `r` from `c`. Thus, given `r` and `c`, we can tell if a point is on the circle by seeing if it is distance `r` from `c`.

The distance between two points `(x_1, y_1)` and `(x_2, y_2)` can be calculated as
`"distance" = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)`
(This formula can be derived using the Pythagorean theorem)

So, the distance between `(0, 0)` and `(5, -2)` is
`sqrt((5-0)^2+(-2-0)^2) = sqrt(25+4) = sqrt(29)`

As `sqrt(29) != 5` this means that `(5, -2)` does not lie on the given circle.