Conics- Circles

Front

What is the standard equation of a circle?

Back

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

Front

What does the center of a circle represent in its equation?

Back

The center of a circle in the equation (x - h)² + (y - k)² = r² is the point (h, k) where the circle is centered.

Front

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

Back

The radius can be found by taking the square root of the constant on the right side of the equation in the standard form (x - h)² + (y - k)² = r².

Front

What is the radius of the circle (x + 3)² + y² = 9?

Back

The radius is 3, since r² = 9, thus r = √9 = 3.

Front

What is the center of the circle (x - 1)² + (y + 2)² = 16?

Back

The center is (1, -2).

Front

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

Back

The equation is x² + y² = 25.

Front

What is the distance between the centers of two circles with equations (x - 2)² + (y - 3)² = 4 and (x + 2)² + (y + 3)² = 9?

Back

The distance is √((2 - (-2))² + ((-3) - 3)²) = √(16 + 36) = √52 = 2√13.

Front

What is the equation of a circle with center (3, -4) and radius 2?

Back

The equation is (x - 3)² + (y + 4)² = 4.

Front

What does the term 'conic sections' refer to?

Back

Conic sections are the curves obtained by intersecting a plane with a double right circular cone, which include circles, ellipses, parabolas, and hyperbolas.

Front

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

Back

Substitute the point (x, y) into the circle's equation. If the result is less than r², the point is inside; if equal, on the circle; if greater, outside.