🧩🎯Equation of a Circle Skill Check

Front

What is the standard form of the equation of a circle?

Back

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.

Front

How do you find the center of a circle from its equation?

Back

The center of a circle in the standard form (x - h)² + (y - k)² = r² is given by the coordinates (h, k).

Front

What is the radius of a circle if its equation is (x + 3)² + (y - 4)² = 16?

Back

The radius of the circle is 4 units, since r² = 16, thus r = √16 = 4.

Front

If the diameter of a circle is 10, what is the radius?

Back

The radius is half of the diameter, so the radius is 5 units.

Front

What are the coordinates of the center of the circle given by the equation (x - 2)² + (y + 1)² = 9?

Back

The center of the circle is at the point (2, -1).

Front

How do you convert the general form of a circle's equation to standard form?

Back

To convert from general form Ax² + Ay² + Bx + Cy + D = 0 to standard form, complete the square for the x and y terms.

Front

What is the equation of a circle with center at (0, 0) and radius 5?

Back

The equation is x² + y² = 25.

Front

What does the term 'completing the square' mean in the context of circles?

Back

Completing the square involves rewriting a quadratic expression in the form (x - h)² + (y - k)² = r² to identify the center and radius.

Front

What is the relationship between the radius and the area of a circle?

Back

The area A of a circle is given by the formula A = πr², where r is the radius.

Front

How can you determine if a point lies inside, on, or outside a circle?

Back

To determine the position of a point (x₀, y₀) relative to a circle with center (h, k) and radius r, calculate the distance from the point to the center: if (x₀ - h)² + (y₀ - k)² < r², the point is inside; if = r², on the circle; if > r², outside.