Conics Memory aid - LEARN Blog
Conics Memory aid - LEARN Blog
Conics Memory aid - LEARN Blog
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Circle<br />
Ellipse<br />
Hyperbola<br />
Parabola<br />
Amanda Rahhal
Circle- Locus<br />
A set of points at a given distance from a point<br />
in a plane
Circle – Rule & parameters<br />
r -> radius
Circle – Rule & Parameters<br />
h -> horizontal shift<br />
(left or right)<br />
X-axis<br />
k -> vertical shift<br />
(up or down)<br />
Y-axis
Ellipse- Locus<br />
locus of all points in the plane whose distances to two<br />
fixed points (the foci) add to the same constant
Ellipse- Rule & parameters<br />
…The locations of a & b will vary according to the graph’s orientation
Ellipse-Rule & parameters<br />
h -> horizontal shift<br />
(left or right)<br />
X-axis<br />
k -> vertical shift<br />
(up or down)<br />
Y-axis
Ellipse- orientation<br />
The orientation of an ellipse depends on parameters a and b…<br />
a > b b > a
Ellipse - Parts<br />
Major<br />
Axis<br />
Semi-major<br />
axis
Ellipse - Parts<br />
Minor<br />
Axis<br />
Semi-minor<br />
axis
Vertices<br />
Ellipse - parts<br />
V1<br />
V1<br />
V2<br />
V2<br />
Co - vertices
Focal Radii<br />
a<br />
Ellipse - Parts<br />
Distance between any point on<br />
ellipse and one of the foci<br />
L1 & L2
F1<br />
Foci<br />
C<br />
F1<br />
F2<br />
C<br />
F2<br />
Ellipse – Parts<br />
C is the<br />
distance<br />
Between the<br />
centre<br />
of an ellipse<br />
And one of<br />
the foci<br />
Finding C<br />
b<br />
Or, if ellipse oriented vertically…<br />
c<br />
a
Hyperbola - Locus<br />
The locus of points the difference of whose<br />
distances from two fixed points is a constant
Hyperbola – Rules and parameters<br />
h -> horizontal shift<br />
(left or right)<br />
X-axis<br />
k -> vertical shift<br />
(up or down)<br />
Y-axis
Hyperbola - Orientation
Hyperbola – Parts
F1<br />
V1<br />
Hyperbola - Parts<br />
V2<br />
F2<br />
Transverse axis<br />
Vertices<br />
Foci<br />
F1<br />
F2<br />
V1<br />
V2
Hyperbola - Parts<br />
The focal radii is one point connecting to the foci in the<br />
hyperbola…
Hyperbola- Parts<br />
Asymptote<br />
Conjugate axis
Hyperbola - Parts<br />
C<br />
C<br />
Finding C
(-a,b) (a,b)<br />
Hyperbola - Rules<br />
The rule of asymptotes is y = slope *x<br />
(-a,b) (a,b)
Parabola - Locus<br />
The locus of a point that is equidistant from a<br />
fixed point(focus) and a fixed line (directrix)
Parabola – Rules and parameters<br />
a > 0<br />
a < 0
Parabola – Rules and parameters<br />
h -> horizontal shift<br />
(left or right)<br />
X-axis<br />
k -> vertical shift<br />
(up or down)<br />
Y-axis
C -> distance between<br />
vertex & focus<br />
F1<br />
Parabola - Parts<br />
Directrix Directrix<br />
F1
Parabola – Parts & Rules<br />
Focus: (0, C)<br />
Directrix: y = -c<br />
Focus: (0, - c)<br />
Directrix: y = c<br />
Focus: (C,0)<br />
Directrix: x = -c<br />
Focus: (-c,0)<br />
Directrix: x = c
Parabola – Parts & Rules<br />
Focus: (h, k + c)<br />
Vertex: (h,k)<br />
Directrix: y = k -c<br />
Focus: (h, k –c)<br />
Vertex: (h,k)<br />
Directrix: y = k +c<br />
Focus: (h +c, k)<br />
Vertex: (h,k)<br />
Directrix: x = h -c<br />
Focus: (h –c,k)<br />
Vertex: (h,k)<br />
Directrix: x = h +c
Parabola – Parts & Rules<br />
Calculate C
The circle on the right’s equation is<br />
Find the missing coordinate.<br />
Practice Problems
The circle on the right’s equation is<br />
Find the missing coordinate.<br />
Practice Problems
Practice Problems<br />
Find the coordinates of the foci of the ellipse
Practice Problems<br />
Find the coordinates of the foci of the ellipse
Practice Problems<br />
Find the rule of the asymptote of this hyperbola
Practice Problems<br />
Find the rule of the asymptote of this hyperbola<br />
(-2,4) (2,4)
Practice Problems<br />
Sketch these two functions:
Practice Problems<br />
Sketch these two functions:
Did you know that with a cone , we can see all four conics?<br />
The images bellow show different “slices” of a cone:<br />
circle, ellipse, parabola and hyperbola!<br />
Source: http://www.mathsisfun.com/geometry/conic-sections.html
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