Graph the following ellipse: 4 ( x − 1 ) 2 + 9 ( y − 2 ) 2 = 36 4\left(x-1\right)^2+9\left(y-2\right)^2=36

In this problem, we're asked to graph the following ellipse. Now, notice that we have this equation given to us right here, and the standard form of an ellipse where we're not at the origin is X minus H2 over A2 plus Y minus K2 over B2 is equal to 1. Now, I can see right off the bat, our equation really doesn't look like this based on what we have, but there is a way we can actually get this form by using some steps in algebra to manipulate our equation. So, what I'm going to do is take every single part of this equation and divide it by 36. I'm allowed to do that as long as I do it on both sides of the equal sign. Now, the reason I'm doing this is because 36/6 gives us 1. Now, notice here that we have 4, this 4 over the 36. We'll ignore the X minus 12 and Y minus 22 for now, because what I'm going to do is recognize something. This 36. Is the same thing as 4 times 9, right? And this 36 is also the same thing as 4 times 9. Now, notice how the 4s will cancel. And those in the next term, the 9s will cancel. So what I can do is write this whole thing as X minus 12/9 plus Y minus 22/4. And notice how we now definitely have this standard form. So all I need to do is find my center, the A and the B values, and then I can graph this. Well, my center is going to be the values that are subtracted from X and Y respectively, which I can see puts my center at 12. And then my A and my B values are going to be what we have underneath the X minus H2 and the Y minus K2 terms. Now, I can see that for A, that's going to be the square root of 9, which is 3, and B is going to be the square root of 4, which is 2. So, let's go over to our graph. My center is going to be at an X value of 1 and a Y value of 2. Now, what I'm going to do next is use my A and my B values to figure out that I need to go 3 units up. So, if I go, or actually, no, this is my A value, so that should be to the right and left. So, actually, it's gonna be 3 units to the right and 3 units to the left. Then it's gonna be 2 units up and 2 units down. So what this is going to do is it's going to give me 1 point here. Well, if we add 3 to 1, we get 4. Now this is going to be back here, so I need to do is subtract 3 from 1, which gives me -2, and then that's going to still be at 2. And then we have our Y values, which is going to be at 1, and then we add 2 to this, so that's going to be at 2, and then we have our next. Value here, which is gonna be at 1, and then we subtract 2 from 2, which is gonna give us 0. And now our ellipse is just going to be connecting all of these points with a smooth curve, giving me the graph of my ellipse. So, that's how you can graph these ellipses from the equation that you have. Hope you found this video helpful, and let's move on.

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객관식

Graph the following ellipse:
$4 {(x - 1)}^{2} + 9 {(y - 2)}^{2} = 36$

Graph of an ellipse centered at (1,2) with points at (0,2), (3,2), (1,5), and (1,-2) on the coordinate plane.

Graph of an ellipse centered at the origin with vertices at (3,0), (-3,0), (0,2), and (0,-2) on labeled axes.

Graph of an ellipse centered at (1,2) with labeled points and x and y axes on a coordinate plane.

Graph of an ellipse centered at (1,2) with labeled points on axes and ellipse perimeter.

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마스터 Ellipses At The Origin Example 1가 Patrick Ford 짧은 영상으로 설명해 줍니다

Prealgebra, Beginning Algebra, & Intermediate Algebra 때문에 힘들어하고 계신가요?

Graph the following ellipse:4(x−1)2+9(y−2)2=364\(\left\)(x-1\(\right\))^2+9\(\left\)(y-2\(\right\))^2=36

다음 시청

Graph the following ellipse:
$4 {(x - 1)}^{2} + 9 {(y - 2)}^{2} = 36$