Warm Up [12/3] - Conic Sections & Matrices

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 and r is the radius.

Front

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

Back

To find the center of a circle from its equation in the form x² + y² + Dx + Ey + F = 0, rearrange it to (x - h)² + (y - k)² = r², where h = -D/2 and k = -E/2.

Front

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

Back

The radius is 4, since r² = 16, thus r = √16 = 4.

Front

Determine the center and radius of the circle: x² + y² - 6x + 8y - 12 = 0.

Back

Center: (3, -4), Radius: 5.

Front

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

Back

The equation is x² + y² = 25.

Front

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

Back

Complete the square for the x and y terms to rewrite the equation in the form (x - h)² + (y - k)² = r².

Front

What are the coordinates of the center and radius of the circle with equation (x + 1)² + (y - 2)² = 9?

Back

Center: (-1, 2), Radius: 3.

Front

What is the radius of the circle given by the equation x² + y² - 4x - 6y + 9 = 0?

Back

The radius is 3.

Front

Write the equation of a circle with center (2, -3) and radius 6.

Back

The equation is (x - 2)² + (y + 3)² = 36.

Front

What is the center of the circle defined by the equation x² + y² + 10x - 4y + 25 = 0?

Back

The center is (-5, 2).