Flashcard: Foundations of Coordinate Geometry — 16 carte

Circle equation — form?

$(x-h)^2 + (y-k)^2 = r^2$.

Hyperbola — graph of?

Inverse proportion function, $ y=rac{k}{x} $.

Vertical line test — purpose?

Checks if a graph is a function.

Standard circle form — features?

Center $(h,k)$ and radius $r$.

Distance formula — definition?

Square root of sum of squared coordinate differences.

Inverse proportion — relationship?

Product of variables is constant ($ xy=k $).

Midpoint — formula?

Average of x's and y's coordinates.

Line equation — from two points?

Use point-slope or two-point formula.

Linear function — form?

$ y = mx + c $, a straight line.

Perpendicular lines — slopes?

Negative reciprocal slopes.

Slope — role?

Indicates line steepness and direction.

Parallel lines — slopes?

Equal slopes, different intercepts.

Inverse proportion graph?

Hyperbola with asymptotes at axes.

Relation vs Function — difference?

Function assigns exactly one y to each x.

Relation — key property?

Set of ordered pairs, may or may not be a function.

Line intersection — method?

Solve equations simultaneously or graphically.