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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step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.