Question

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

Answer 1

The general equation of the ellipse with a vertical major axis is,
 
                               (y^2) / (a^2) + (x^2) / (b^2) = 1

where a and b are halves of the major and minor axis, respectively.

With the given above, the equation becomes,
                               (y^2) / (3^2) + (x^2) / (2^2) = 1
     
                                (y^2) / 9 + (x^2) / 4 = 1

Multiplying the whole equation with 36, the final equation becomes,

                                      4y^2 + 9x^2 = 36

Answer 2

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

Answer: y² + 16x² = 1

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