Identify the equations of ellipses whose major axis lengths are twice their minor axis lengths.

Mathematics

1 answer:

madreJ [45]2 years ago

5 0

The equations of ellipses whose major axis lengths are twice their minor axis lengths are

(x - h)²/4b² + (y - k)²/b² = 1 and
(x - h)²/b² + (y - k)²/4b² = 1

To answer the question, we need to know what an ellipse is.

<h3>What is an ellipse?</h3>

An ellipse is part of a conic section.

<h3>The equation of the ellipse</h3>

The equation of an ellipse centered at (h,k) with major axis on the x-axis and major axis length, 2a and minor axis length 2b is

(x - h)²/a² + (y - k)²/b = 1

<h3>The equation of ellipse with major axis x-axis</h3>

The equations of ellipses whose major axis lengths are twice their minor axis lengths with ellipse centered at (h,k) with major axis on the x-axis. Since the major axis is twice the length of the minor axis, a = 2b.

So, (x - h)²/a² + (y - k)²/b² = 1

(x - h)²/(2b)² + (y - k)²/b² = 1

(x - h)²/4b² + (y - k)²/b² = 1

<h3>The equation of ellipse with major axis y-axis</h3>

The equations of ellipses whose major axis lengths are twice their minor axis lengths with ellipse centered at (h,k) with major axis on the y-axis. Since the major axis is twice the length of the minor axis, a = 2b.

So, (x - h)²/b² + (y - k)²/a² = 1

(x - h)²/b² + (y - k)²/(2b)² = 1

(x - h)²/b² + (y - k)²/4b² = 1

So, the equations of ellipses whose major axis lengths are twice their minor axis lengths are