Graph each equation. (x^2)/(16)+(y^2)/(9)=1

Name: Problem 18, Chapter 10: Intermediate Algebra
Uploaded: 2020-08-05T14:44:48-08:00
Duration: 3 min 29 s
Channel: James Schroeder
Description: Graph each equation. (x^2)/(16)+(y^2)/(9)=1

Key Concepts

Standard Form of an Ellipse Equation

The standard equation for an ellipse centered at the origin is written as x²/a² + y²/b² = 1, where 'a' and 'b' represent the distances from the center to the ellipse's vertices along the horizontal and vertical axes, respectively. This form is fundamental to identifying the key parameters of the ellipse, such as its axes lengths and position.

Graphing Techniques for Ellipses

Graphing an ellipse involves determining its center, major axis, and minor axis from the standard form of its equation, and then plotting key points such as the vertices along these axes. Once these points are identified, a smooth, oval curve is drawn to reflect the symmetry and shape of the ellipse.

Ellipse

An ellipse is a type of conic section defined as the set of all points in a plane for which the sum of the distances to two fixed points (the foci) is constant. It exhibits symmetry along both its major and minor axes, and its shape is determined by these distances.

Transcript

00:01 Hello there.

00:02 In this problem we're being asked to graph an equation.

00:05 I've written it down here the equation is x squared over 16 plus y squared over 9 equals 1.

00:12 Now when it and graphed it using an online grapher you can do that or you can use your graphing calculator or even do it manually but we'll talk about a couple of important things here so remember the standard form this is an ellipse.

00:25 We can see it's an ellipse just by the shape of it but a couple of things that are important let's look at the standard form.

00:31 Let's look at the standard form.

00:31 Form for an ellipse and that's going to be x minus h squared over a squared plus y minus k squared over b squared equals one that's the center then is at hk the major axis has a radius of a and the minor axis has a radius of b.

01:13 So these are the important things that we can do to either get a quick sketch of a graph or to check and make sure our work is accurate.

01:20 So i'm going to keep working in green here.

01:22 And you can see that from our equation, h and k are both zero.

01:29 So there's no, there's no term on this x and y.

01:34 And so h and k are both zero.

01:36 So the center for this graph is at at 0 .0.

01:42 We got that point marked here, center at 0.

01:48 We know that a squared is the major, a is the major axis, a squared is equal to 16.

01:57 And so a is a square root of 16 or four...