... Major Axis : The line segment AA in which the focii S and S lie (of length 2a) is called the major axis
of the ellipse. Point of intersection of major axis with directrix is called the foot of the directrix (z and z ).
Minor Axis : The y-axis intersects the ellipse in the points B (0, b ) and ...
... in the figure, for any P’ on l the distance to l’, |P’L’| ≤
|P’L| ≤ |P’F| + |FL|, where |FL| is the distance from F to l’. Hence, |P’L’|
- |P’F| ≤ |FL| and the difference is largest (=|FL|) when point P belongs
to the perpendicular FL from point F to l’.
The optical property of the hyperbola. Suppos ...
... y = a(x-h)2 + k
Students will learn about each of the components in the above standard form of a quadratic and what impact
they will have on the graph of y = x2 from a transformation point of view.
a : the vertical stretch/compression factor and vertical reflection component
if a > 1, then parabola ...
... For a given angle of incoming light (), we observe that rays that intersect the parabola
near the vertex make reflections that intersect each other near the bottleneck (Figure 3);
while rays that intersect the parabola farther from the vertex make reflections that
intersect each other farther from ...
... ____ T9 (A1): Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a
figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on
the circle centered at the origin and containing the poin ...
... The tangent line of a parabola at either endpoint of its latus rectum forms an angle of π4 with the
latus rectum. As such, parabolas G1 and G2 share the same tangent at C1 , and similarly parabolas
G2 and G3 share a tangent at C3 . At cusp C2 , however, we obtain two different tangent directions.
... Joel D. Leger,1,a) Clara M. Nyby,1,a) Clyde Varner,1 Jianan Tang,1 Natalia I. Rubtsova,1 Yuankai Yue,1
Victor V. Kireev,1 Viacheslav D. Burtsev,1 Layla N. Qasim,1 Grigory I. Rubtsov,2 and Igor V.
... Students work with parabolas whose vertex is on the origin as well as off the origin and they
work with parabolas that open not only up and down, but also to the left and to the right. For
these, they graph the parabola by writing two functions.
Students will derive general equation for parabolas, f ...
... Parabola: the set of all points in a plane which are equidistant from a fixed point F, called
the focus, and a fixed line d (not containing F), called the directrix.
Axis of symmetry of a parabola: the line through the vertex perpendicular to the directrix
quadratic equation: ax2 + bx + c = 0
to sol ...
... 5. Go to the second function in the drop down menu, a parabola. Find the area when a=0 and
b=4. Find the area when a=-4 and b=4. (The E-14 indicates exponential notation, so the value in
the second window is essentially 0). What property of the parabola accounts for the reported area
when a=-4 and b ...
... Finding Vertex Form is very easy in this case! That is because in this case, general form and
vertex form are identical. I could express my function in the following way to make vertex form
even more recognizable:
... The axis runs through the midpoint of (0, 8) and (4, 8).
You can easily see this point to be (2, 8). (You don’t need
to use the midpoint formula for this.) The equation for the
axis of symmetry is x = 2 .
... our straightedge to draw a unique straight
line that passes through both of the points
• Given any fixed point in the plane, and any
fixed distance, we can use our compass to
draw a unique circle having the point as its
center and the distance as its radius
... intersection of two parabola tangents lies on a line parallel to the parabola’s
axis, and passing through the midpoint of the chord joining the points of
tangency. (This is easily established from the equation y 4p1 x 2 of the parabola
with focus F0, p , directrix y "p and axis x 0. )
It fol ...