Task Sets: Equation of a circle (standard form, completing the square) - Digital SAT Math

Recall / Warm-Up

Which of the following is the correct expansion of $(a + b)^2$ ?

$a^2 + b^2$

$a^2 + 2ab + b^2$

$a^2 - 2ab + b^2$

$2a + 2b$

The distance formula gives the distance between $(1, 2)$ and $(4, 6)$ as
$d = \\sqrt{(4-1)^2 + (6-2)^2}$ .
Compute $d$ .

To complete the square on $x^2 - 8x$ : take half of $-8$ , which is ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ , then square it to get ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .
Add this to get $(x - \\_\\_\\_)^2$ .

half coefficient:

square of half:

value in factored form:

Fluency Practice

A circle has center $(2, -5)$ and radius $3$ .
What is the value of $r^2$ in its standard-form equation $(x - 2)^2 + (y + 5)^2 = r^2$ ?

A circle has center $(-3, 4)$ and passes through the origin $(0, 0)$ .
What is the radius of the circle?

What is the center of the circle $(x + 1)^2 + (y - 7)^2 = 36$ ?

$(1, 7)$

$(1, -7)$

$(-1, 7)$

$(-1, -7)$

What is the radius of the circle $(x - 4)^2 + (y + 3)^2 = 49$ ?

$49$

$24.5$

$7$

$\\sqrt{24.5}$

A circle has the equation $x^2 + y^2 = 25$ .
What are the coordinates of the center? Enter your answer as an ordered pair (e.g., $(0, 0)$ ).

Equation of a Circle — Practice Set

Recall / Warm-Up

Fluency Practice