Geometri Analitik Fase F | Persamaan Lingkaran Bagian 2 - Kedudukan Titik Terhadap Lingkaran

Assalamualaikum Wr. Wb. Meet again with me, Denny Hadayani on the MATLAB channel. In this video, I will continue the discussion of the second part of the circle material, namely the position of the point towards the circle. For those of you who have not studied the first part, please check the video link in the description of this video.

Okay, now we discuss the importance of the point towards the circle. Okay, in this video we will learn

The material of the position of the point towards the circle There are three possibilities of the position of the point towards the circle The first point is located in the circle So the position of the point is in the circle So the position can be anywhere friends Which is definitely in the circle Like this Then the second possibility The point is located in the circle It means that the point is passed by the circle

And the third possibility is the point is located outside the circle So the position is outside the circle How is the concept? Quite simple The first, if the point is located in the circle

You just need to substitute the coordinate of the point to the equilibrium of the circle and the sign becomes less than So the value will be smaller than the fingers squared This is if the circle is centered at 0.0 Then how if the circle is centered at A, B? The method is the same So later the sign is less than, which means the value is smaller than the fingers squared

Likewise, if the shape of the circle is in the general form, the value is the same, it is less than So for the point is placed in the circle, then this is the sign of less than The second position, if the point is placed in the circle, then this sign remains the same

Still the same, both circles centered at 0.0, and circles centered at A, B. Likewise if the circle is in the form of a general, the sign remains the same. Well, if the point is located outside the circle for the third position or the third position, then the sign changes to "more than". This is also the same, "more than". The general form is also the same, "more than". Well, this is the position of the point towards the circle.

So what you need to remember, in the circle, the sign is less than or smaller, located in the circle is equal to, and located outside the circle means the sign is more than or larger. To make it clearer, pay attention to the following examples. Okay, the first example, determine the position of the next points towards the circle x^2 + y^2 = 25. This is a circle centered at 0.0.

we will look for the positions of points A, B, and C in this circle how? friends, substitute the coordinate of these points in the left section of the circle so friends, substitute to this part yes these 3 coordinates, we start from the point A coordinate -2.4 we substitute to this circle equation, x squared + y squared

Or x1 squared plus y1 squared where this is x1, this is x1, 4 is y1 So x1 squared, negative 2 squared, y1 squared, 4 squared Negative 2 squared is 4, 4 squared is 16, 4 plus 16 is 20 Now let's compare it with R squared, R squared is 25

It turns out that 20 is smaller than 25, so this is less than R squared If less than, it means that point A is located in the circle Okay, let's try point B Point B, 4,-3, the way is the same, we substitute the circle's equation X1 squared plus Y1 squared, X1

4, yes, one is negative 3 4 squared plus negative 3 squared 4 squared 16, negative 3 squared 9 16 plus 9, 25, compared to R squared R squared is 25 too, so this is the same as 25 Oh, it means the same as R squared If it's the same, it means point B is located in the circle

Now we try the coordinate point C, 5, -1 Now we substitute the circle equation We replace x1 with 5, y1 with -1 So 5 squared plus -1 squared 5 squared is 25, -1 squared is 1, so the result is 26 We compare with the R squared R squared is 25

26 is actually larger than 25, which means the point C is located outside the circle because the value is larger than R^2 Easy right? Now let's try the second example

Okay, now we discuss the second example, here is the question of UTBK 2019. Point A 1.1 located outside or exterior of the circle area x squared plus y minus a squared equals 5. The value of a that is possible is, well, this is outside the circle, so you just have to substitute, we replace x with 1, y with 1.

Enter this equation and the sign we change with more than because outside the circle So we multiply x squared, we replace x with 1, 1 squared plus y minus a squared, we replace the y with 1 too, 1 minus a squared, the sign we replace with more than 5

1 squared, 1 and 1 minus a squared is 1 minus 2a plus a squared more than 5 1 plus 1, 2 or we change the position so a squared minus 2a plus 2 is more than 5 The second row we subtract 5 so we get a squared minus 2a minus 3 is more than 0 Now this is the inequality of the square, we find or factor, we find the creator of the zero

So, a + 1 times a - 3 is more than 0, then we get a - 1 or a 3. Of course, you have learned the square root of the equation. If not, please study the video first, I will include it in the description of this video. Well, here, a is less than -1 or a is more than 3. Which one is the full one? 4, this is more than 3, so this is the full one.

3 is not complete Then -2 is less than -1, so this is complete And -1 is not complete So the answer is 1 and 3, 1 and 3 only The answer is B

For those of you who are still having difficulty in the equation like this, we can also work on this matter in another way by checking the choices of answers one by one. But still, we change the x and y first with 1 and y is also 1. So we get x squared is 1 squared plus y. We replace it with 1, 1 minus a squared, the sign is more than 5.

1 squared is the result of 1 plus 1 minus a, just let it be, don't do anything 1 minus a squared is more than 5, we lose 1, we move the space or the second space we reduce 1

1 minus a squared is more than 5 minus 1 is 4 Now, friends check all possible values ​​a Find the value that is more than 4 We try, we try the 4, choose 1 a is replaced by 4, it means 1 minus 4 is negative 3, negative 3 squared Oh, that means the first one is negative 3 squared 9 Fulfill more than 4 Then we check if 3

1 - 3 = -2, -2 squared, the result is 4 The second, this is the result is 4 We look for more than 4, it means this is not complete Then the third, -2, replace the a with -2 1 - -2 = +3, 3 squared, 9, 9 is more than 4

The third one is 9, it turns out to be more than 4, it fulfills Then the fourth one is negative 1, the a is replaced by negative 1 1 minus negative 1 is 2, 2 squared, the result is We look for more than 4, it means it doesn't fulfill, so the answer is still 1 and 3 only

To understand this matter, please try these 5 questions and the explanation can be found in the description of this video. Okay, that's all for this video, see you in the next video. Assalamualaikum Wr Wb