A conic or conic section is a plane curve that can be obtained by intersecting a cone with a plane that does not go through the vertex of the cone. There are three possibilities, depending on the relative position of the cone and the plane. If no line of the cone is parallel to the plane, the intersection is a closed curve, called an ellipse. If one line of the cone is parallel to the plane, the intersection is an open curve whose two ends are asymptotically parallel; this is called a parabola. Finally, there may be two lines in the cone parallel to the plane; the curve in this case has two open pieces, and is a hyperbola. In mathematics, parametric equations bear slight similarity to functions: they allow one to use arbitrary values, called parameters, in place of independent variables in equations, which in turn provide values for dependent variables. A simple kinematical example is when one uses a time parameter to determine the position, velocity, and other information about a body in motion. Abstractly, a relation is given in the form of an equation, and it is shown also to be the image of functions from items such as R. It is therefore somewhat more accurately defined as a parametric representation. It is part of regular parametric representation. Converting a set of parametric equations to a single equation involves solving one of the equations usually the simplest of the two for the parameter. Then the solution of the parameter is substituted into the remaining equation, and the resulting equation is usually simplified. It should be noted that the parameter is never present when the equation is in singular form; it must cancel out during conversion. Or, the process put simply: the simultaneous equations need to be solved for the parameter, and the result will be one equation. Additional steps need to be performed if there are restrictions on the value of the parameter. The arc length of a circle is the distance from one point on the circumference to...

...AN INTRODUCTION TO CONICSECTIONS
There exists a certain group of curves called ConicSections that are conceptually kin in several astonishing ways. Each member of this group has a certain shape, and can be classified appropriately: as either a circle, an ellipse, a parabola, or a hyperbola. The term "ConicSection" can be applied to any one of these curves, and the study of one curve is not essential to the study of another. However, their correlation to each other is one of the more intriguing coincidences of mathematics.
A CONICSECTION DEFINITION
Put simply, a conicsection is a shape generated when a cone intersects with a plane. There are four main types of conicsections: parabola, hyperbola, circle, and ellipse. The circle is sometimes categorized as a type of ellipse.
In mathematics, a conicsection (or just conic) is a curve obtained as the intersection of a cone (more precisely, a right circular conical surface) with a plane. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2. There are a number of other geometric definitions possible. One of the most useful, in that it involves only the plane, is that a conic consists of those points whose distances to some point, called a focus, and...

...Chapter 13_Graphing the ConicSections
Ellipses
In this study guide we will focus on graphing ellipses but be sure to read and understand
the definition in your text.
Equation of an Ellipse (standard form)
Area of an Ellipse
( x − h) 2 ( y − k ) 2
+
=1
a2
b2
with a horizontal axis that measures 2a units, vertical axis
measures 2b units, and (h, k) is the center.
The long axis of an ellipse is called the major axis and the short
axis is called the minor axis. These axes terminate at points that
we will call vertices. The vertices along the horizontal axis will be
( h ± a, k ) and the vertices along the vertical axes will be ( h, k ± b) .
These points, along with the center, will provide us with a method
to sketch an ellipse given standard form.
A = π ab
Graph
( x − 5) 2 ( y − 8) 2
+
=1
9
25
First plot the center.
Then use a = 3 and
plot a point 3 units to
the left and 3 units to
the right of the
center.
Use standard form to
identify a, b, and the
center (h, k).
Next, use b = 5 and
plot a point 5 units up
and 5 units down
from the center.
Label at least 4
points on the ellipse.
In this example the major axis is the vertical axis and the minor axis is the horizontal
axis. The major axis measures 2b = 10 units in length and the minor axis measures
2a = 6 units in length. There are no x- and y- intercepts in this example.
Problems Solved!
13.4 - 1
Chapter...

...
1.
(a) Indications
-The stenopaic slit refraction is useful for confirming the results of other refraction techniques for patients with irregular astigmatism or reduced visual acuity.
- It is helpful for patients who have difficulty understanding the complex instructions associated with other subjective techniques.
-It is important to note that, like the pinhole, the stenopaic slit may be used diagnostically to determine a patient's potential visual acuity.
-The astigmatism present in the patient’s old spectacles should be considered
-The small amount of cylindrical power is of little consequences, in that the subjective end point can quickly be rechecked after the stenopaic slit is removed
(b) Techniques
Axis determination
i. remove cylinder power from retinoscopy and
ii. identify BVS or MPTMV, VA
iii. fogged the patient (F=1/2 CYL + 0.50 DS) and watch the acuity chart
iv. put the stenopaic slit at any position
v. the slit is rotated until acuity is maximized. The slit now lies along the minus cylinder axis.
Spherical power
vi. with the slit in this position, the fog is reduced to best acuity.
vii. the lens in place is the sphere power of the patient’s lens formula (pt’s final sphere)
viii. the slit is rotated 90 degrees. This will fog the patient again
viiii. the fog is again reduced to best acuity. The algebraic difference between the power of the lens in place at the end of this operation and the lens power in place at the end of step one is the minus cylinder...

...The parabola has an electromagnetic signal reflection property. Four signals are shown in green and blue. These signals are shown with arrows on both ends to indicate the focus either collects the signals (coming in) or the focus generates the signals and they leave in parallel from the parabola. The inside of the parabola can be a mirror (for light) or another material (for non visible electromagnetic waves.)
As light enters parallel to axis of symmetry it will strike the parabola and reflect toward the focus. You can see heavy black line segments drawn on the parabola on the lines tangent to the parabola at the points of incidence. Two angles are formed between each of these segments and the light striking and bouncing off; each pair of angles are equal and depend upon the location the light hits the parabola.
Imagine the focus is a light bulb and the parabola a mirror. The light bulb emits light in all directions. All the light that strikes the parabola will leave parallel to the axis of symmetry. Spot lights make use of this property.
Of course a a parabolic mirror is 3-dimensional. Imagine rotating the parabola about its axis of symmetry and you will get a shape you'll recognize as the headlight of your car.
Light emitted from the focus leaves the parabolic mirror in parallel paths, shown below. Headlights, spotlights, etc., have the shape of a parabola to increase the intensity of the light and direct the light.
The ellipse...

...Chapter 10 : Quadratic Relations and ConicSections
History of ConicSections
History of ConicSections
Apollonius of Perga (about 262-200 B.C.) was the last of the great mathematicians of the golden age of Greek mathematics. Apollonius, known as "the great geometer," arrived at the properties of the conicsections purely by geometry. His descriptions were so complete that he would have had little to learn about conicsections from our modern analytical geometry except for the improved modern notation. He did not, however, describe the properties of conicsections algebraically as we do today. It would take almost 2000 years before mathematicians would make great advances in the understanding of conicsections by combining both geometric and algebraic techniques.
Apollonius defined the conicsections as sections of a cone standing on a circular base. The cone did not have to be a right cone, but could be slanted, or oblique. Apollonius noticed that all sections cut through such a cone parallel to its base were circles. He then extended the properties that he observed from these circles to ellipses and the other conicsections. He even solved the difficult problem of finding the shortest...

...separates from the choroid after a retinal
tear develops.
Retinal detachment is a serious eye condition. If it is not treated, it can lead to
blindness. Each year, 30,000 people in the United States are diagnosed with retinal
detachment.
There are clear warning signs that a person is developing a retinal tear or
detachment. When diagnosed early, most retinal problems are treatable. With
treatment, retinal problems usually do not affect vision very much.
This reference summary explains what retinal tears and detachments are. It discusses
their symptoms, causes, diagnosis and
Lens
treatment options.
Cornea
Anatomy
It is important to recognize the parts of the
eye before learning about retinal tears and
detachments. This section reviews the
anatomy of the eye.
Light hits the cornea of the eye first. The
cornea is the transparent covering on the
front of the eye.
Iris
Vitreous
Macula
Retina
Next, light travels to the back part of the eye through the pupil. The pupil is the
opening in the center of the iris, the colored part of the eye.
This document is a summary of what appears on screen in X-Plain™. It is for informational purposes and is not intended to be a substitute for the advice
of a doctor or healthcare professional or a recommendation for any particular treatment plan. Like any printed material, it may become out of date over
time. It is important that you rely on the advice of a doctor or a healthcare...

...Delos Santos
Members
Anna Lyn P. Jaime
Parametric and Non-Parametric Test
Topics
I. Introduction
II. Summary of the major points and how they might affect statistical analysis
III. What is the Parametric and Non- Parametric Tests?
A. Parametric
a. Definition
b. Parametric Assumption
B. Non-Parametric
a. Definition
b. NonParametric Assumption
c. Two Different Meaning of Parametric Test
IV. Measurement
A. What are the 4 levels of measurement discussed in Siegel’s Chapter?
a. Nominal or Classificatory Scale
b. Ordinal or Ranking Scale
c. Interval Scale
d. Ratio Scale
V. When do we use the Parametric and Non-Parametric Test?
A. Parametric Test
a. Nominal or Ordinal
B. Non Parametric Test
b. Interval or Ratio
VI. Kinds of Tests
A. Parametric Test
a. ANOVA- Analysis of Variance
i. Assumptions
ii. Inventor
1. Sir R. A. Fisher (1935)
iii. Formula
b. Test of Test
i. Inventor
1. Satterthwaite’s T-test(1946)
ii. Formula
B. Non – Parametric Test
a. Wilcoxon signed rank test
b. Whitney- Mann- Wilcoxon(WMW) test
c. Kruskal Wallis (KW)test
d. Friedman’s test
I. Introduction
If you’ve...

...1:
Write the equations for the x and y-axes.
Answer :
The y-coordinate of every point on the x-axis is 0.
Therefore, the equation of the x-axis is y = 0.
The x-coordinate of every point on the y-axis is 0.
Therefore, the equation of the y-axis is x = 0.
Question 2:
Find the equation of the line which passes through the point (–4, 3) with slope .
Answer :
We know that the equation of the line passing through point , whose slope is m, is .
Thus, the equation of the line passing through point (–4, 3), whose slope is , is
Question 3:
Find the equation of the line which passes though (0, 0) with slope m.
Answer :
We know that the equation of the line passing through point , whose slope is m, is .
Thus, the equation of the line passing through point (0, 0), whose slope is m,is
(y – 0) = m(x – 0)
i.e., y = mx
Question 4:
Find the equation of the line which passes though and is inclined with the x-axis at an angle of 75°.
Answer :
The slope of the line that inclines with the x-axis at an angle of 75° is
m = tan 75°
We know that the equation of the line passing through point , whose slope is m, is .
Thus, if a line passes though and inclines with the x-axis at an angle of 75°, then the equation of the line is given as
Question 5:
Find the equation of the line which...