Level 496 Level 498
Level 497

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A=√(x₁-x₂)²+(y₁-y₂)²
Distance formula
x²+y² = r²
Equation of a circle with center at (0,0)
(x-h)²+(y-k)²=r² (center at h,k)
Standard Equation of a circle with radius "r"
x²+y²+Dy+Ey+F=0
General Equation of a circle
Standard equation of a Parabola with center at 0
x=y² (opens left or right) y=x² (opens up or down)
x=a(y-k)²+h
Standard Equation of a Parabola
General form of a Parabola
y=ax²+bx+c (quadratic) (Opens up or down depending on ± a)
x²/a²+y²/b²=1
Equation of an ellipse with center at (0)
(x-h)²/a²+(y-k)²/b²=1
Standard equation of ellipse
Ax²+By²+Cx+Dy+E=0
General equation for ellipse
largest denominator is "Y"
An ellipse is vertical if
largest denominator is"X"
An ellipse is horizontal if
Minor Axis
The shorter axis on an ellipse with co vertices
Major Axis
The longer axis on an ellipse with vertices
x²/a²-y²/b²=1
Equation of hyperbola with center at (0,0)
(x-h)²/a²-(y-k)²/b²=1
standard equation of a hyperbola
ax²-by²+cx+dy+e=0
general equation of a hyperbola
horizontally
hyperbola - if x² is positive then hyperbola opens
vertically
hyperbola - if y² is positive then hyperbola opens
hyperbola xy=k means
hyperbola does not intersect x or y axis
Circle
r= asin(theta)
Ellipse
Hyperbola
Equation subtracts x²/a and y²/b=1; x and y coefficients have different signs.
Parabola
the graph of a quadratic function
y-y₁=m(x-x₁)
Point-Slope form
Conic Sections
Curves found by cutting a cone with a plane.
vertex
The point where two sides meet. (Shared end points of the line segments of a polygon.)
Center
Each regular polygon has a center because it can be inscribed in a circle.
Focus (Foci - plural)
One of two fixed points at the centers of an ellipse.
Asymptote
An imaginary line on a graph that acts as a boundary line.
Conic Section
A curve formed by the intersection of a plane and a double cone resulting in a circle, ellipse, parabola, and hyperbola.
(x-h)^2+(y-k)^2=r^2
Standard Form of an Equation of a Circle