Identify type of conic and more

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In summary, the conversation discusses identifying the type of conic and finding its vertices, foci, directrix, and asymptotes for the equation e=45/(10+9sin(θ)). Through graphing in polar mode, it is determined that the conic is an ellipse and it is suggested to convert the polar equation to Cartesian coordinates and then rearrange it for easier calculation.
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Identify type of conic and more...

Homework Statement


Identify the type of conic, find the vertices, the foci, directrix, and asymptotes (if they exist) for the equation e=45/(10+9sin(θ))

Homework Equations


As far as equations I don't know of any to help me find which type of conic, or any characteristics of this.

The Attempt at a Solution


Graphing in polar mode, I find that it is an ellipse.
I think we have to convert it from a polar equation into Cartesian coordinates.
 
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I assume e is what's normally written as r in polar.
Multiply out the equation. Then try rearranging it so that when you square both sides every occurrence of r is either as r2 or as r sinθ.
 

Related to Identify type of conic and more

1. What is a conic?

A conic is a two-dimensional curve that is formed by intersecting a plane with a cone. It can be classified as a circle, ellipse, parabola, or hyperbola.

2. How do you identify the type of conic?

The type of conic can be identified by its equation. A circle has an equation in the form of (x-h)^2 + (y-k)^2 = r^2, an ellipse has an equation in the form of (x-h)^2/a^2 + (y-k)^2/b^2 = 1, a parabola has an equation in the form of y = ax^2 + bx + c, and a hyperbola has an equation in the form of (x-h)^2/a^2 - (y-k)^2/b^2 = 1.

3. What is the focus and directrix of a conic?

The focus is a fixed point on a conic that is used to define its shape and position. The directrix is a fixed line that is used to construct the conic. For a circle and ellipse, the focus is at the center and the directrix is a line perpendicular to the major axis. For a parabola, the focus is located at the vertex and the directrix is a horizontal line. For a hyperbola, there are two foci and two directrices.

4. How does a conic relate to real-world situations?

Conics are commonly seen in real-world situations such as satellite orbits (ellipses), the shape of a parabolic dish (parabola), and the path of a comet (hyperbola). They also have applications in engineering, physics, and astronomy.

5. What is the difference between a degenerate conic and a non-degenerate conic?

A degenerate conic is a special case of a conic where the plane and cone intersect at a point, resulting in a single point or no points at all. Examples of degenerate conics include a point (circle with radius of 0), a line (ellipse with a = b), and two intersecting lines (hyperbola with a = b). A non-degenerate conic is a regular conic that has a distinct shape, such as a circle, ellipse, parabola, or hyperbola.

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