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# canonical formulas of conical sections and their properties

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Please see the attached file for the fully formatted problems.

1. Solve the system of equations algebraically. Be sure to find all
solutions!
X^2+y^2=10
2x^2-y^2=17

I got not sure if it's right or missing
x=2.999999976132
Y=0.999999870315

2. Find the coefficient of the term x^5 y^3 in the expansion of (4x-y)^8
3. Put each conic in standard form; identify the conic, , state
vertices, centers, asymptotes where applicable.

1) x^2 = 4y&#8722;8

Standard Form:

Identify which Conic Section:

Characteristics applicable:
Center:

Vertices:

Asymptotes:

2) 9(x&#8722;2)^2&#8722;16(y+1)^2=144
Standard Form:
Identify which Conic Section:

Characteristics applicable:

Center:

Vertices:
Asymptotes:

4(x&#8722;3)^2+25(y+2)^2=100
Standard Form:

Identify which Conic Section:

Characteristics applicable:

Center:

Vertices:

Asymptotes:

##### Solution Summary

The solution shows how the coefficients of canonical form of certain conical sections relate to their attributes.

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