I don't want or need help unless I ask for it; this is just notes and stuff.
Circle: a set of points that are equidistant from a fixed point. In plain English, it's perfectly round blob with points on it.
Standard form of the circle equation: (x-h)^2 + (y-k)^2 = r^2
(h,k) is the center of the circle and r is the radius.
To write the equation when given a circle on a graph, look at where the center is, determine the coordinates, and find out how much the radius is (distance from the center to any point on the circle).
General form of the equation of a circle: x^2 + y^2 + ax + by + c = 0.
To find general form: complete the square.
Focus: fixed point that the parabola "eats". *munch munch* The focus lies on the axis of symmetry, which is a line cutting the parabola in half.
Directrix: a line perpendicular to the axis of symmetry
Vertex: where the parabola starts. It's halfway between the focus and directrix.
A parabola is a little U-shaped thing that goes wheeeee and isn't this definition the most helpful ever
They always have the word problems with the searchlights and other lights because searchlights are apparently super important in life because wow I always wondered how far across the average searchlight is
Parabola equation: (x-h)^2 = 4p(y-k)
(y-k)^2 = 4p(x-h)
The (x-h)^2 ones are the up/down ones. The "normal" ones. (y-k)^2 ones are weird and sideways and gahhhh
In these equations, the variable "p" is the distance between the vertex and the focus or the vertex and the directrix (the distance is the same for both).
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- Lahash -
Also known as Samurai
Est. January 2014
Author of the Path of Legends series - coming 2020!
"Fear not in this Time of Chaos, this War of Darkness. For on the horizon, there shines a light, a light brighter than any before . . ."