Circle Equation Flashcard

The standard equation of a circle is given by: $$(x - h)^2 + (y - k)^2 = r^2$$ .

To convert a quadratic expression into binomial form, complete the square or factor the expression.

The expansion is $$x^2 - 2ax + a^2$$ .

The radius r can be found from the equation $$(x - h)^2 + (y - k)^2 = r^2$$ as r = $$\text{sqrt}(r^2)$$ .

The center (h, k) represents the point in the Cartesian plane around which the circle is drawn.

From the equation $$(x - h)^2 + (y - k)^2 = r^2$$ , the center is (h, k) and the radius is r.

Completing the square involves rewriting a quadratic in the form $$x^2 + bx$$ as $$(x + \frac{b}{2})^2 - \frac{b^2}{4}$$ .

The expansion is $$y^2 - 2by + b^2$$ .

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

To convert from general form $$Ax^2 + Ay^2 + Bx + Cy + D = 0$$ to standard form, complete the square for x and y.