Front

What is the standard equation of a circle with center (h, k) and radius r?

Back

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

Front

How do you find the midpoint of a line segment with endpoints (x1, y1) and (x2, y2)?

Back

The midpoint M is calculated using the formula: $$M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$$.

Front

What is the formula for the inverse of a linear function f(x) = mx + b?

Back

The inverse function is given by: $$f^{-1}(x) = \frac{x - b}{m}$$.

Front

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

Back

The radius is the square root of the right side of the equation: $$r = \sqrt{16} = 4$$.

Front

What is the center of the circle represented by the equation (x + 2)^2 + (y - 5)^2 = 25?

Back

The center of the circle is at the point (-2, 5).

Front

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

Back

Expand and rearrange: $$(x - h)^2 + (y - k)^2 = r^2$$ becomes $$x^2 + y^2 + Dx + Ey + F = 0$$.

Front

What is the distance formula between two points (x1, y1) and (x2, y2)?

Back

The distance d is calculated as: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$.

Front

What is the significance of the coordinates in the midpoint formula?

Back

The coordinates represent the average position of the endpoints of a line segment.

Front

How do you identify the center and radius from the equation of a circle?

Back

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

Front

What is the process to find the inverse of the function f(x) = \frac{8x - 3}{5}?

Back

To find the inverse, swap x and y, then solve for y: $$y = \frac{5x + 3}{8}$$.