# Identifying types of conics

Not what you're looking for?

For each of the equations identify the type of conic it is and list the major features associated with this type of conic

Major Features

Circles

- Find the coordinates of the center

- Find the length of the radius

- Find the length of the diameter

Parabolas

- Find the coordinates of the vertex

- Find the coordinates of the focus

- Write the equation of the axis of symmetry

- Write the equation of the directrix

Ellipses

-Find the center of the ellipse

- Fine the coordinates of both of the foci points

- Find the coordinates of alll the vertices

- Find the length of the major axis

-Find the length of the minor axis

Hyperbolas

- Find the center

-Find the coordinates of the twp vertices

-Find the coordinates of the two foci points

- Find the equation of the two asymptotes

Equations

1) X62 - 10x +2y^2 +40y - 175=0

2) 2x^2 + 6x + 5y^2 - 40y - 7 = 0

3) 5x^2 - 80x + 5y^2 - 30y - 135 = 0

4) 6x^2 + 24x + 3y - 45 = 0

##### Purchase this Solution

##### Solution Summary

This provides four equations and shows how to identify which type of conic section each one is.

##### Solution Preview

2.26

1. x^2 - 10x + 2y^2 + 40y -175 = 0 Rewriting...

(x^2-10x) + 2 (y^2+20y)- 175 = 0

Completing the square...

(x^2-10x+25)-25 + 2(y^2+20y+100)-100 -175 = 0

(x-5)^2 + 2(y+10)^2 = 200 Putting in a standard form...

(x-5)^2/200 + (y+10)^2/100 = 1

This is an ellipse with major axis a = 200 and minor axis b = 100

Center is at (5,-10)

Foci are (+ -a e,0)

We have b^2 = a^2 [1-e^2] from this e = sqrt[1- b^2/a^2] = sqrt(3)/2

Foci are, (+ - 100*sqroot(3),0)

That is, x-5 = +- 100* sqroot(3)==> x = (+ -) 100*sqrt(3)+5

and y+10 = 0 ==> y = -10 are the co- ordinates of ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

##### Probability Quiz

Some questions on probability

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.