Irisan Kerucut - Parabola • Part 1: Definisi, Unsur-Unsur, dan Jenis-Jenis Parabola

Welcome to the Science Window channel. In this video we will discuss the "Circle Slice" or Parabola, the first part, namely about the definition of elements and types of parabolas. Keep watching this video until the end. This is the outline of the "Circle Slice". We enter the second "Circle Slice", namely the parabola. First, we discuss the definition of parabolas.

A parabola is a place where the points are located at the same distance from a certain point and line. This particular point is called a focus or a fire point of a parabola, or labeled with an F.

while the line is called the directrix line or the direction line, which is labeled as line G. So, for example, there is a red parabola, this red parabola is opened to the right, like the shape of the letter C. Here, the focus point of the parabola is this.

So the parabola's focus point is always inside the parabola. And the direction line or the G-director line is outside the parabola, like this. Okay? So, according to the definition, every point on the parabola is the same distance from the focus point and the direction line. For example, here is point A. Point A is located on the parabola.

then the distance from point A to point F, the focus point, will be the same as the distance from point A to line G. Remember, if the distance from point A to line G has to be straight, so it has to be the closest distance, don't be tilted like this or like this. So I give a zigzag sign. So A to F is the same as A to G. Yes, here I give the same sign like this. Next, for example, another example.

There is a point B, the point B is also placed on the parabola, then the distance from B to F or BF is the same as the distance from B to the line G. So BF is the same as B to G, this is also straight.

but the distance bf or bg is not the same as af or ag, the same is the distance from the point to the focus point and the point to the line, but if you compare af and bf, it's not the same, because it's a different point, right? Next, for example, here is a point c, the point c is also placed on the parabola, so the distance cf is the same as the distance from c to line g or line of the directrix, this is a square, then the sign is like this.

Okay, and then, so the point is all points, for example, the point D here or the point E, the point G, the point K, every point placed on the parabola has the property of the distance from the focus point is the same as the distance to the direction line or the line of the G-director. Okay, do you understand?

Next we go to the elements of the parabola. So actually the point of focus F and the direction line or the line of the G-directrix are also elements of the parabola. But we have discussed the definition of the parabola earlier. Now we discuss other elements of the parabola.

The first is the source of symmetry of the parabola, namely the line that divides the parabola into two equal parts. So, if the parabola is opened to the right like this, then the symmetry source or the line that divides the parabola into two equal parts, logically, is this line, the horizontal line. In this case, we divide the line by h.

The line H is a symmetry sum of parabolas because the line H divides the parabola into two equal parts, the upper part and the lower part. The upper part, if reflected against the line H, becomes the lower part and vice versa. So in this case, the symmetry sum of parabolas is line H.

Okay? Symmetry sum also consists of a line that passes through the point of focus F and straight with the line of the G-directrix. This line H, the parabola symmetry sum, passes through the point of focus F and straight, a straight line with the direction line or the line of the G-directrix. That's the nature of symmetry sum. Okay, next. There is a vertex or vertex, labeled with a point P.

is a point of a parabola with a symmetry sum. Point P means this, the point of the top of the parabola is a cut between the parabola and the symmetry sum. Yes, so here is point P or the top of the parabola or vertex. Next, there is another name, the latus rectum or in short LR, which is the shortest rope through the point of focus F.

The rope is a loop, remember? We learned it in circles. So if there is a circle here, then the rope is a straight line that connects two points that are placed in a circle. So, for example, there is a point A,

this has a point B, then the A-B slant rope is like this, a straight line that connects two points located in a circle. If the slant rope is straight, if the curved one is slant, right? Well, on the parabola, the principle is the same. A straight line that connects two certain points located on the parabola. Well, because here the latus rectum is the shortest slant rope that passes through the focus point F, so here, where is the focus point F? Here.

The slant line that passes the point of focus F is not much. It can be straight like this, it can be slightly inclined like this, it can be inclined downwards like this, it can be inclined like this, and so on. There are many slant lines made through the point of focus F. But here, the latus rectum is the shortest slant line that passes the point of focus F. Which is the shortest? The shortest is this one.

So the rope is described here as a green line, namely L1-L2. So here L1-L2 is the latus rectum of this parabola. So if you look at the nature of the latus rectum, it is parallel to the direction line or the directrix line and straight towards the symmetry line. Okay, do you understand?

Next, we go to the types of parabolas. So far, I have always explained that I always use parabolas that are opened to the right, right? The shape is like the letter C. It turns out that the parabola can also be opened to the left, up, or down. And here, I group them into a horizontal parabola and a vertical parabola.

The horizontal parabola is a parabola that is opened to the right or left, because if it's right, left is horizontal, right? While the vertical parabola is a parabola that is opened up or down, because the top and bottom are vertical. Well, here, if you look at the horizontal parabola, the direction line or the direction line is vertical. While the symmetry sum, or the line H here, is horizontal.

while if the vertical parabola is the opposite, the vertical parabola, both the one that opens up and down, the direction line or G or the directrix is horizontal and the symmetry sum or the line H here is vertical. Okay, next we will see the position of the focus point and the directrix. The parabola opens to the right, the focus point is on the right of the peak point, F on the right is P, while G is the direction line on the left is P.

Okay, if the parabola is opened to the left, the opposite is the focus on the left of the top, the line of direction G on the right of the top. So G always opposes the direction of the opened parabola. Opened to the right, G on the left, opened to the left, G on the right. If the focus is appropriate, because remember the focus point is placed inside the parabola. So if the parabola is opened to the right, the focus point is on the right of the top point.

if the parabola is opened to the left, the focus point is on the left of the top point. Understand? The same goes for vertical parabolas. If the parabola is opened upwards, the focus point is above the top point and the direction line or directrix below the top point. While the parabola is opened downwards, the focus point is below the top point and the direction line or directrix line above the top point.

Okay, that's it for this video. To see the complete playlist from this book, you can click the playlist thumbnail on the top right. If you have any questions, suggestions, or criticisms, you can write them in the comments column. Hopefully useful and see you in the next video.