What is the standard form equation of the ellipse with vertices at (0, 6) and (0, -6) and co vertices at (4, 0) and (-4, 0)?

Solution:

Given, the vertices are (0 6) and (0, -6) and co vertices are (4, 0) and (-4, 0)

We have to write the standard form equation of the ellipse.

The equation of an ellipse with its major axis on the x-axis and minor axis on the y-axis is given by

x²/a² + y²/b² = 1

Where, a is the length of semi major axis

b is the length of semi minor axis

According to the question,

Major axis, a = 6

Minor axis, b = 4

Now, a² = 6² = 36

b² = 4² = 16

Now, the equation of the ellipse can be written as

x²/36 + y²/16 = 1

Therefore, the required standard equation is x²/36 + y²/16 = 1.

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What is the standard form equation of the ellipse with vertices at (0, 6) and (0, -6) and co vertices at (4, 0) and (-4, 0)?

Summary:

The standard form equation of the ellipse with vertices at (0, 6) and (0, -6) and co vertices at (4, 0) and (-4, 0) is x²/36 + y²/16 = 1.