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Chapter 13: Problem 47

What is an ellipse?

Short Answer

Expert verified
In geometry, an ellipse is a curve on a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. It can be perceived as a circle elongated along one direction.

Step by step solution

01

Understanding basic geometry concepts

Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. An understanding of the general concept of a shape and space is necessary in order to define and identify an ellipse.
02

Defining an ellipse

An ellipse is a shape that results from the intersection of a cone and a plane that cuts through both halves of the cone. This shape is a curve on a plane that surrounds two focal points. The sum of the distances from any point on the ellipse to the two focal points remains constant.
03

Identifying an ellipse

An ellipse looks quite similar to a circle, but it is more elongated. If you were to draw a circle and then pull it apart while keeping the center fixed, you'd get an ellipse.

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Most popular questions from this chapter

Will help you prepare for the material covered in the next section. Solve: \(x^{2}=2(3 x-9)+10\)

Use the vertex and intercepts to sketch the graph of each equation. If needed, find additional points on the parabola by choosing values of y on each side of the axis of symmetry. $$x=-3(y-5)^{2}+3$$

The equation of a parabola is given. Determine: a. if the parabola is horizontal or vertical. b. the way the parabola opens. c. the vertex. $$x=-(y+3)^{2}+4$$

Use a graphing utility to graph the parabolas. Write the given equation as a quadratic equation in \(y\) and use the quadratic formula to solve for \(y .\) Enter each of the equations to produce the complete graph. $$y^{2}+10 y-x+25=0$$

How can you distinguish ellipses from circles by looking at their equations?
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