In, On or Outside the given Circle
This a classic nugget on the SAT! You’ll need to select the point that lies either INSIDE, ON or OUTSIDE of a given circle. So, do you think you’ll be given the graph of the circle? Ha ha! Of course not! And given the time constraints of the exam, sketching out the circle graph and then roughly evaluating different given points probably won’t cut it. So you will need the elegant hack that we cover in this video.
Interactive Video
It’s All About Insertion
To test any given point–
Just insert its x- and y-coordinates into the given CIRCLE equation. In other words, if the given point is (2,-3), then replace “x” in the circle equation with 2, and replace “y” in the equation with negative three. Then solve for that expression. And finally, compare that value with the given radius squared value!!
- LESS than RADIUS >> POINT is INSIDE
- EQUAL to RADIUS >> POINT is ON
- GREATER than RADIUS >> POINT is OUTSIDE
