Select the correct equations in the image. Identify the ellipses, represented by equations, whose eccentricities are less than 0.5.

  equations 1, 2, 6 . . . (top two, bottom right)

Step-by-step explanation:

For the standard-form equation of an ellipse:

  Ax^2 +Bx +Cy^2 +Dy +E = 0

we can define ...

  p = min(A, C)

  q = max(A, C)

Then the eccentricity can be shown to be ...

  e = √(1 -p/q)

  p/q = 1 -e^2

For eccentricity < 0.5, we want ...

  p/q > 3/4

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Checking the values of p/q for the given equations left-to-right, top-to-bottom, we have p/q = ...

Equations 1, 2, 6 are of ellipses with eccentricity < 0.5.

beanburito

step-by-step explanation: