Equations of Circles

Front

What is the standard equation of a circle?

Back

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

Front

What does (h,k) represent in the standard circle equation?

Back

(h,k) is the center of the circle.

Front

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

Back

The radius is the square root of the number on the right side of the equation (r = √r²).

Front

In the equation (x-4)²+(y-3)²=25, what is the radius?

Back

The radius is 5.

Front

In the equation (x-4)²+(y-3)²=25, what is the center of the circle?

Back

The center is (4, 3).

Front

What is the distance formula used for in relation to circles?

Back

The distance formula is used to find the distance between two points, which can help determine if a point lies inside, on, or outside a circle.

Front

What is the general form of a circle's equation?

Back

The general form is x² + y² + Dx + Ey + F = 0.

Front

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

Back

You can complete the square for both x and y terms to convert to standard form.

Front

What does the term 'radius' refer to in a circle?

Back

The radius is the distance from the center of the circle to any point on its circumference.

Front

What is the significance of the point (0,0) in the context of circles?

Back

(0,0) is the center of a circle when the equation is in the form x² + y² = r².