Solve by Table/Function Regression

Circle Equation Constant Term on the SAT: Desmos Walkthrough

This lesson uses Desmos tables and regressions: drop the given values into a table, fit the model with a regression line, and read the constants straight off the fit.

A real SAT-style question

How to solve it in Desmos, step by step

1. 1

   Step 1

   Type the equation exactly as given. Desmos instantly draws the full circle.

   Type in Desmos

   $x^{2}+14x+y^{2}=6y+109$
2. 2

   Step 2

   Type this point to mark the center of the circle. Desmos plots a dot at the middle of the circle.

   Type in Desmos

   $c=\left(-7,3\right)$
3. 3

   Step 3

   Click the rightmost edge of the circle, on the same level as the center. Desmos snaps to a gray point and shows its coordinates as about 5.92 comma 3. Type that point.

   Type in Desmos

   $e=\left(5.92,3\right)$
4. 4

   Step 4

   Let Desmos measure the distance from the center to that edge point. Type this line and Desmos shows about 12.92, which is the square root of 167. So the radius is the square root of 167. The answer is C.

   Type in Desmos

   $d=\operatorname{distance}\left(c,e\right)$

Now you try one

Same question type, different numbers. Use the exact Desmos moves from the walkthrough above.

More Desmos SAT lessons