Explore BrainMass

Explore BrainMass

    Identifying types of conics

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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

    © BrainMass Inc. brainmass.com February 24, 2021, 2:20 pm ad1c9bdddf
    https://brainmass.com/math/synthetic-geometry/identifying-types-of-conics-15043

    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 ...

    Solution Summary

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

    $2.19

    ADVERTISEMENT