Find an equation in standard form for the ellipse with the vertical major axis of length 6 and minor axis of length 4.

One of the equations of ellipse is in a form of the lengths of its axes. If we have the length of its major axis as 2a and the length of its minor axis as 2b then, the values of a and b are,

    2a = 16,   a = 16/2 = 8

    2b = 4,     b = 4/2 = 2

Given that we have the major axis as vertical, the equation for ellipse is,

      y²/a² + x²/b² = 1

Substituting,

     y²/8² + x²/2² = 1

Simplifying,

    y² + 16x² = 1

y² + 16x² = 1

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m∠a is 90°

m∠b is 40°