Equation of a circle Practice Questions (Grade 10)

Question 1easy

What is the radius of $(x - 3)^{2} + (y + 1)^{2} = 16$ ?

$r^{2} = 16$ , so $r = 4$ .

Question 2easy

A circle has equation $(x + 8)^{2} + (y - 3)^{2} = 49$ . What is the $x$ -coordinate of its center?

$(x + 8)^{2} = (x - (-8))^{2}$ , so the center's $x$ -coordinate is $-8$ .

Question 3easy

What is the $y$ -coordinate of the center of the circle $(x + 1)^{2} + (y - 7)^{2} = 4$ ?

$(y - 7)^{2}$ means $k = 7$ ; the center is $(-1, 7)$ .

Question 4easy

What is the diameter of the circle $(x - 2)^{2} + (y - 7)^{2} = 36$ ?

$r = \sqrt{36} = 6$ , so the diameter is $2r = 12$ .

Question 5easy

For the circle $(x - 1)^{2} + (y - 4)^{2} = 81$ , what is the value of $r^{2}$ ?

In standard form the right-hand side equals $r^{2}$ , so $r^{2} = 81$ .

Question 6easy

What is the radius of the circle $(x - 3)^{2} + (y + 2)^{2} = 25$ ?

The right-hand side is $r^{2} = 25$ , so $r = \sqrt{25} = 5$ .

Question 7easy

A circle is centered at the origin and passes through the point $(6, 8)$ . What is its radius?

The radius is the distance from $(0, 0)$ to $(6, 8)$ : $\sqrt{36 + 64} = \sqrt{100} = 10$ .

Question 8easy

The graph of the equation $(x - 7)^{2} + (y - 3)^{2} = 25$ is a circle in the coordinate plane. The point $(a, b)$ lies on the circle. Which of the following is a possible value for $a$ ?

The center is $(7, 3)$ and the radius is $5$ . A point on the circle must satisfy $|a - 7| \le 5$ , so $2 \le a \le 12$ . The value $9$ is in this interval.

Equation of a circle practice

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