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    CP02 Conics

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    Admin Anak Panah

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    © All Rights Reserved
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    CP02 Conics

    Uploaded by

    Admin Anak Panah
    4 views2 pages

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    © © All Rights Reserved

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    4 views2 pages

    CP02 Conics

    Uploaded by

    Admin Anak Panah

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
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    Defining Parameters

    Define the type of conic (Parabola, Hyperbola, Ellipse, or Circle) based on the given
    equation. If the conic is a hyperbola, provide the equation of the asymptotes. For each
    conic, also determine the vertex, the directrix, and if applicable the foci. Finally, sketch
    the conic.
    1.4 x 2+ 4 y 2=32
    Define the hyperbola and directrix equation based on the eccentricity and the parabola
    equation given. Determine the foci, vertex, directrix, the asymptotic line of the equation
    and sketch the graph.
    1. e=4, y 2=−x
    Complete The Square
    Define the type of conic (Parabola, Hyperbola, Ellipse, or Circle) based on the given
    equation. If the conic is a hyperbola, provide the equation of the asymptotes. For each
    conic, also determine the vertex, the directrix, and if applicable the foci. Finally, sketch
    the conic.
    1.4 x 2−8 x+12 y 2 +20 y +28=0
    2. 12 x2 +54 x−4 y 2 +64 y−200=0
    Defining Equation
    Define the conic equation from the given parameters and sketch the conic.

    1. Vertical Hyperbola with eccentricity √2 that passes through (1,2)


    2
    2. Ellipse with a vertex at (5,0) that passes through (2,3)
    3. Hyperbola with asymptotes 2x + y = 0 and 2x - y = 0; vertex at (5,0)
    4. Horizontal ellipse that goes through (0,3) and (-5,-2)

    Rotation of Conic
    Find the new equation of the conic after rotated by the θ specified. Sketch the conic
    before and after the rotation.
    2 π
    1. y =2 x ,θ=
    3
    Given the equation below, use the rotation method to eliminate the xy in the equation
    and sketch the new graph.
    1. x 2−2 xy+ y 2−17=0
    Parametric Representation of Curve on Plane
    Determine the corresponding curve of the parameter equation specified and sketch its
    graph.
    1. x=4 co s2 t , y=4 sin 2 t ; 0 ≤ t ≤ π

    Evaluate the indicated double integrals.

    1.
    Sketch the indicated region S manually and find its area using double integrals.
    Note: answer without double integrals will only obtain at most 10 points.
    1.
    Sketch the solid enclosed by the indicated region R and the given plane, then use
    double or triple integrals to find its volume.

    1.

    Sketch the given Tetrahedron in the 1st octant enclosed by the coordinate
    planes and the given plane, then calculate its volume using triple
    integrals.
    Note: answer without triple integrals will only obtain at most 15 points.
    1.

    Use jacobian to evaluate the given double integrals in the indicated region S.
    Hint:

    1. where is the region enclosed by

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