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canonical formulas of conical sections and their properties

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−8

Standard Form:

Identify which Conic Section:

Characteristics applicable:
Center:

Vertices:

Asymptotes:

2) 9(x−2)^2−16(y+1)^2=144
Standard Form:
Identify which Conic Section:

Characteristics applicable:

Center:

Vertices:
Asymptotes:

4(x−3)^2+25(y+2)^2=100
Standard Form:

Identify which Conic Section:

Characteristics applicable:

Center:

Vertices:

Asymptotes:

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Solution Summary

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

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