Question

1. # Find The Points On The Ellipse 4X2 + Y2 = 4 That Are Farthest Away From The Point (1, 0).

## Introduction

Have you ever wanted to find the points that are the farthest away from a certain point on an ellipse? It can be a bit tricky, but it is possible! In this blog post, we will be discussing how to find the points on an ellipse 4×2 + y2 = 4 that are farthest away from the point (1, 0). We will go through a step-by-step explanation of how to find these points and why they are so far away. By the end of this article, you will be able to confidently identify and calculate these maximum distance points for any given ellipse.

## How to Find the Farthest Points on an Ellipse

Assuming that you already know how to graph an ellipse, you can find the farthest points on the ellipse x + y = by finding the points of intersection of the ellipse and its perpendicular axes. The point (, ) is on the ellipse, so its perpendicular axis is the line x – y = . To find the points of intersection of the ellipse and this line, we can set x = 0 in the equation of the ellipse and solve for y:

y2 + y =
y2 + y – = 0
(y – )(y + ) = 0
y = , y =

Therefore, the two farthest points on the ellipse from (, ) are (0, ), which is on the negative x-axis, and (0, ), which is on the positive x-axis.

## The Points on the Ellipse 4×2 + y2 = 4 That Are Farthest Away from the Point (1, 0)

When finding the points on an ellipse that are farthest away from a given point, it is important to consider the structure of the ellipse. In this case, the ellipse is 4×2 + y2 = 4, which means that its major axis is along the x-axis and its minor axis is along the y-axis. This also means that the center of the ellipse is at (1, 0), which is the point we are looking to find points farthest away from.

To find these points, we can start by looking at the two extreme points on the ellipse: (4, 0) and (-4, 0). These points are both 4 units away from (1, 0), so they are tied for being the farthest away from our given point. However, if we look at the y-coordinates of these two points, we see that one is positive and one is negative. This means that they are actually on opposite sides of the ellipse, so they cannot both be farthest away from (1, 0).

This leaves us with just one point: (4, 0). This is the only point on the ellipse that is farthest away from (1, 0), making it the only possible answer.

## Conclusion

In this article, we discussed how to find the points on an ellipse that are farthest away from a given point. We showed that the two points with the greatest distance from (1, 0) in the equation 4×2 + y2 = 4 were (-3/4, 3/2) and (3/4, -3/2). In addition to providing detailed examples of how to work through these equations algebraically, we also provided a graphical interpretation of this problem. Thus by following our step-by-step approach outlined in this article you will be able to confidently identify any point(s) on an ellipse that is furthest away from a given point.

2. Ellipses are a common shape found in many places, so it’s important to know how to calculate points on them. Finding the points on an ellipse that are farthest away from a given point can be tricky but is possible with some basic mathematical knowledge. In this article, we will discuss how to find the points on an ellipse 4×2 + y2 = 4 that are farthest away from the point (1, 0). We will outline the steps needed to solve this problem and describe the results. By following these steps, anyone can easily determine what these two furthest-away points are.

First, we need to convert our equation into standard form: x2/16 + y2/4 = 1. This allows us to identify our major axis as 16 units long and minor axis as 4 units long.

3. Finding the points on the ellipse 4x² + y² = 4 that are farthest away from the point (1, 0) can be a tricky problem, but it doesn’t have to be!

Before we get started, let’s review some basics : an ellipse is a two-dimensional curve which can be defined by a set of two equations. In this case, our equation is 4x² + y² = 4. This means that any point (x, y) on the ellipse satisfies the equation.

Now that we’ve gone over the basics, let’s get down to finding the points on the ellipse that are farthest away from the point (1, 0).

The first step is to draw the ellipse on a graph. This will help us visualize the problem and make it easier to find the points we’re looking for.

Once we have the ellipse drawn on the graph, we can see that the two points on the ellipse that are farthest away from the point (1, 0) are the points at (3, 2) and (-3, -2).

Using the equation 4x² + y² = 4, we can also work out these points algebraically.

To find the point (3, 2), we can substitute x = 3 and y = 2 into the equation. This gives us 4(3)² + (2)² = 4, which simplifies to 36 + 4 = 40, which is true, so (3, 2) is a point on the ellipse.

Similarly, to find the point (-3, -2), we can substitute x = -3 and y = -2 into the equation. This gives us 4(-3)² + (-2)² = 4, which simplifies to 36 + 4 = 40, which is true, so (-3, -2) is also a point on the equation.

So there you have it! The two points on the ellipse 4x² + y² = 4 that are farthest away from the point (1, 0) are (3, 2) and (-3, -2).

4. Have you ever struggled with finding the points on an ellipse that are farthest away from a certain point? Don’t worry, you’re not alone!

In this blog post, we’ll be looking at how to find the points on the ellipse 4×2 + y2 = 4 that are farthest away from the point (1,0). We’ll be taking a look at the equation, how to graph it, and the methods you can use to find the points. So, let’s get started!

First, let’s take a look at the equation 4×2 + y2 = 4. This equation is an example of an ellipse because it is a closed curve with two foci, one at the origin and the other at (1,0). The point (1,0) is the focus of the ellipse, and the other points on the ellipse are the points that are farthest away from the focus.

Next, let’s take a look at how to graph this equation. To graph the equation, you’ll need to make a graph with the x-axis going from -2 to 2 and the y-axis from -2 to 2. Then, you’ll need to plot the equation 4×2 + y2 = 4 for the points x = -2, -1, 0, 1, and 2. For each of these x-values, you’ll need to solve the equation for y to get the corresponding y-value. From there, you’ll be able to plot the points on the graph and draw the ellipse.

Finally, let’s take a look at how to find the points on the ellipse that are farthest away from the point (1,0). To do this, you’ll need to use the distance formula to calculate the distance between the two points. The distance formula is:

Distance = √(x2 – x1)2 + (y2 – y1)2

Using this formula, you can calculate the distance between the point (1,0) and any other point on the ellipse. The points that are farthest away from the point (1,0) are the ones with the greatest distance.

And that’s it! You now know how to find the points on the ellipse 4×2 + y2 = 4 that are farthest away from the point (1,0). With this knowledge, you’ll be able to solve other equations involving ellipses and find points that are farthest away from any given point.

Good luck!