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What is the value of c? | SAT Circles Practice | Lumist

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What is the value of c?

SAT Circles practice question

Geometry and TrigonometryMedium

A circle in the $xy$ -plane has its center at $(-4,4)$ and has a radius of 6. An equation of this circle is $x^2+y^2+ax+by+c=0$ , where $a$ , $b$ , and $c$ are constants.

What is the value of $c$ ?

Enter a number or fraction, e.g. 5, 0.5, 1/2

Explanation

Setup: Start from standard form with center $(-4,4)$ and radius $6$ .

Solve: $(x+4)^2+(y-4)^2=36$ . Expand: $x^2+8x+16+y^2-8y+16=36$ . So $x^2+y^2+8x-8y-4=0$ , and $c=-4$ .

Answer: $-4$

Common slips:

Using $36$ as $c$ instead of moving all terms to one side.
Forgetting to square the center coordinates.
Dropping the signs in $(x+4)$ or $(y-4)$ .

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