Question

Bonus Is the point (-3, -5) inside, outside, or on the circle whose equation is (x + 7)² + (y − 2)² = 62? (SOMEONE PLEASE EXPLAIN!!)

Answer 1

Outside

Explanation:

Answer 2

Outside, as the distance between the point and the center of the circle is more than the radius.

Explanation:

Equation of a circle:

The equation of a circle has the following format:

`(x-x_0)^2 + (y-y_0)^2 = r^2`

In which
`(x_0,y_0)` is the center and r is the radius.

Testing if a point is inside the circle:

Point (x,y), we replace in the equation. If it is less than the radius squared(in this case, 62), it is in.

In this question:

Point (-3,-5). So

`(-3+7)^2 + (-5-2)^2 = 4^2 + (-7)^2 = 16 + 49 = 65`

The square distance of the point to the center is of 65, which is more than the square of the radius, meaning that the point is outside the circle.