Question

Given the point s (-2, 12) and the circle ( x 2) 2 ( y - 3) 2 = 81, where would point s be found? interior of the given circle exterior of the given circle on the given circle insufficient information

Answer 1

Point S (-2, 12) lies outside the circle defined by the equation (x - 2)^2 + (y - 3)^2 = 81, as the result of substituting S's coordinates into the equation is greater than the radius squared.

Step-by-step explanation:

The student asks where the point S (-2, 12) would be found in relation to the circle defined by the equation (x - 2)2 + (y - 3)2 = 81. This is a standard form equation for a circle centered at (2, 3) with a radius of 9. To determine the position of point S related to this circle, we need to substitute the coordinates of S into the circle's equation and compare the result to the radius squared.

For point S (-2, 12), we substitute and get:
(-2 - 2)2 + (12 - 3)2 =
42 + 92 =
16 + 81 = 97.

Since 97 is greater than the radius squared (81), point S lies outside the circle. Therefore, point S is in the exterior of the given circle.