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    canonical formulas of conical sections and their properties

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    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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    https://brainmass.com/math/basic-algebra/canonical-formulas-conical-sections-properties-218953

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

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