Parabola notes pdf

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# Parabola notes pdf

Standard form of equation of Parabola. How to graph a Parabola? Menaechmus was first to discover a method to solve the problem about the doubling of cube with using parabolas. Archimedes figured out the area surrounded by a parabola and a line segment Apollonius gives the name "parabola". Pappus proved the properties of the focus and directrix of the parabola.

Parabola is basically a curve or path followed by a ball when it got kicked. Altogether it means the shape or curve made by kicking or throwing a ball in the air. Parabola is an open curve at the intersecting surface of the cone.

Parabolic Curve is defined with the help of a point and a line. Parabolic curve is a locus of all the points on the plane which have same distance from a line called Directrix and a fixed point called Focus. A parabola does not have a center. Here, F is the fixed point called focus, l is the fixed line called Directrix. P 1P 2 and P 3 are the different points on the plane. This shows that the distance from focus to point on plane and to directrix is equidistant for all the points on plane.

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Parabola is a special case of ellipse in which one of the foci is at the point of infinity. Axis of Symmetry - It is a line which divides the parabola in two equal parts that is, it is the line of symmetry of parabola. It is perpendicular to the directrix and passes through the focus. At vertex the parabola is abruptly curved. It is the reflective property of parabola which makes it useful in so many fields.

The rays of light or sound which are parallel to the axis of symmetry get reflected to the focus after touching the surface of the plane. Uses of Parabola:. If the focus lies on the directrix, so that the same distance of directrix and focus together form a straight line then it is the degenerate case of parabola. The vertex lies on the axis of symmetry and perpendicular to the directrix.

Focus of Parabola: Focus is a point from which the distance is measured to form conic. The parabola has the vertex as the midpoint of the focus and the directrix. Eccentricity of Parabola: Eccentricity is the factor related to conic sections which shows how circular the conic section is. More eccentricity means less spherical and less eccentricity means more spherical.

The eccentricity of parabola is the ratio of the distance between the focus and a point on the plane to the vertex and that point only. It is perpendicular to the axis of symmetry. In parabola, let a is the distance from focus to the vertex, which is equidistant from the vertex to directrix.Vertex at 0,0. The circle circumscribing the triangle formed by any three tangents to a parabola passes through the focus.

The area of the triangle formed by three points on a parabola is twice the area of the triangle formed by the tangents at these points. A circle circumscribing the triangle formed by three co-normal points passes through the vertex of the parabola and its equation is given by. The two vital parabolas along with their basic components like vertex and directrix are tabulated below:. DearPreparing for entrance exams? Register yourself for the free demo class from askiitians. Studying in Grade 6th to 12th?

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Latest articles from Blog. New dates to be released See More. Xpress Buy Xpress Buy. Get Free Sample Now. Current Grade : --Select-- 6 7 8 9 10 11 12 12th pass. Target Year : --Select-- Christopher-Nevis-Anguilla St. Helena St. Lucia St. Pierre and Miquelon St. State :. City :. Landline No :. Message :.In this section we want to look at the graph of a quadratic function. The most general form of a quadratic function is. The graphs of quadratic functions are called parabolas. Here are some examples of parabolas. Note as well that a parabola that opens down will always open down and a parabola that opens up will always open up. In other words, a parabola will not all of a sudden turn around and start opening up if it has already started opening down.

Similarly, if it has already started opening up it will not turn around and start opening down all of a sudden. The dashed line with each of these parabolas is called the axis of symmetry. Every parabola has an axis of symmetry and, as the graph shows, the graph to either side of the axis of symmetry is a mirror image of the other side. This means that if we know a point on one side of the parabola we will also know a point on the other side based on the axis of symmetry.

We will see how to find this point once we get into some examples. We should probably do a quick review of intercepts before going much farther. We also saw a graph in the section where we introduced intercepts where an intercept just touched the axis without actually crossing it.

Finding intercepts is a fairly simple process.

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So, we will need to solve the equation. There is a basic process we can always use to get a pretty good sketch of a parabola.

Here it is. Now, there are two forms of the parabola that we will be looking at. This first form will make graphing parabolas very easy.

Unfortunately, most parabolas are not in this form. The second form is the more common form and will require slightly and only slightly more work to sketch the graph of the parabola. There are two pieces of information about the parabola that we can instantly get from this function. Be very careful with signs when getting the vertex here.

Okay, in all of these we will simply go through the process given above to find the needed points and the graph. First, we need to find the vertex. We will need to be careful with the signs however. Therefore, the vertex of this parabola is. We solve equations like this back when we were solving quadratic equations so hopefully you remember how to do them.

Now, the left part of the graph will be a mirror image of the right part of the graph.

Conics: Graphing and Analyzing The Parabola: Section 10.2 Ex 1

If we are correct we should get a value of It was just included here since we were discussing it earlier. Again, be careful to get the signs correct here!

This one is actually a fairly simple one to graph. Now, the vertex is probably the point where most students run into trouble here. However, as noted earlier most parabolas are not given in that form.Hyperbola is an important topic from JEE point of view.

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Conic section constitutes questions every year in JEE Main in which one question is from hyperbola. Read and revise all the important topics from hyperbola. Download the pdf of the Short Notes on Hyperbola from the link given at the end of the article.

Hyperbola is the locus of a point in a plane such that the difference of its distance from two fixed point in the same plane is always constant. Transverse axis TA : The line segment containing the foci is known as the transverse axis and the length is 2a. Conjugate axis CA : The line segment containing the points B 1 and B 2 is called as conjugate axis and the length is 2b.

Focal axis: Line containing the fix points F 1 and F 2 called as foci is called as the focal axis. Focal length: The distance between F 1 and F 2 is called the focal length.

Corresponding to every hyperbola there exist a hyperbola such that the conjugate axis and the transverse axis of one is equal to the transverse axis and the conjugate axis of the other. Such hyperbolas are called as the conjugate hyperbola. If, hyperbola, H:. Then conjugate hyperbola, CH:. If e 1 is the eccentricity of the hyperbola and e 2 is the eccentricity of the conjugate hyperbola then. This hyperbola is also known as an equilateral hyperbola.

The circle described on the transverse axis of the hyperbola as the diameter is called an auxiliary circle. These two points: P and Q are called as the corresponding point and Q is called the eccentric angle of the point P.

The equation of chord of contact will be similar to that of the tangent. Thus a line when touches the hyperbola will be tangent and the same line when cuts the hyperbola will be the chord of contact. However, rotating the coordinate axis through an angle of 45 0we get another form of this rectangular hyperbola. Thus, the equation is.

Engg Exams. Hyperbola Hyperbola is the locus of a point in a plane such that the difference of its distance from two fixed point in the same plane is always constant. Vertices: A 1 a,0 and A 2 -a,0 Focal axis: Line containing the fix points F 1 and F 2 called as foci is called as the focal axis Focal length: The distance between F 1 and F 2 is called the focal length Focal chord: A chord passing through a focus is called the focal chord.

Conjugate Hyperbola Corresponding to every hyperbola there exist a hyperbola such that the conjugate axis and the transverse axis of one is equal to the transverse axis and the conjugate axis of the other.

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Auxiliary Circle and Eccentric angle The circle described on the transverse axis of the hyperbola as the diameter is called an auxiliary circle. From 'T' a tangent is drawn on the auxiliary circle, meeting the circle at Q. This suggests that from a given point P h,k we can draw at maximum two tangents. Now, director circle can be imaginary or real. Chord of contact The equation of chord of contact will be similar to that of the tangent. Rectangular Hyperbola This is a special kind of hyperbola when the length of traverse and conjugate axis are equal.

Member since Oct Related Posts.A parabola is the set of points in a plane that are the same distance from a given point and a given line in that plane. The given point is called the focus, and the line is called the directrix. The midpoint of the perpendicular segment from the focus to the directrix is called the vertex of the parabola. The line that passes through the vertex and focus is called the axis of symmetry see Figure 1. In Form 1, the parabola opens vertically. Refer to Figure 1 a. The distance from the vertex to the focus and from the vertex to the directrix line are the same. This distance is. A parabola with its vertex at hkopening vertically, will have the following properties. In Form 2, the parabola opens horizontally. Refer to Figure 1 b. A parabola with its vertex at hkopening horizontally, will have the following properties.

State which direction the parabola opens and determine its vertex, focus, directrix, and axis of symmetry. The equation is the same as. Factor out the coefficient of y 2 from the terms involving y so that you can complete the square. Add this amount to the left side to keep the equation balanced. Previous Quiz Circle. Next Quiz Parabola. Removing book from your Reading List will also remove any bookmarked pages associated with this title.

Are you sure you want to remove bookConfirmation and any corresponding bookmarks? My Preferences My Reading List. Algebra II.It is one of those topics in your JEE Main Maths preparation in which if you can assure quick and easy marks. Download the Parabola notes PDF from the link given below. Parabola is the locus of a point such that the distance remains the same from the line called the directrix.

Let P x, y be any point on the parabola. Then by definition. It should be seen that the second degree terms in the general equation of a parabola forms a perfect square. Let P be any point h, k. Now P will lie outside, on or inside the parabola according as k 2 -4ah greater than, less than or equal to zero. Solving the line and parabola, we get.

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Suppose y 1y 2y 3 be the ordinates of the feet of these co-normal points, then. Engg Exams. Note : The other forms of the parabola with latus rectum 4a are. Also, the point at 22at is referred to as the parametric point on the parabola. The position of a Point w. Some standard results on the Parabola i The tangents at the extremities of a focal chord of a parabola intersect at right angles on the directrix.

SP Diameter The locus of the middle points of a system of parallel chords is called a diameter. Looking to further boost your JEE Main prep? Member since Oct Related Posts.At Pregame, the big ones go by names like Fezzik, Goodfella, Spartan, Sleepyj, VegasButcher, and King Creole. In July 2014, Bell patted himself on the back when he announced on Pregame a new standard for his touts: They had to publicly provide their real name and a signed declaration declaring any past legal troubles.

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