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kiruha [24]
2 years ago
8

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

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

Learn more about ellipse here:

brainly.com/question/25950359

#SPJ4

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Step-2 : Find two factors of  -60  whose sum equals the coefficient of the middle term, which is   -11 .

     -60    +    1    =    -59

     -30    +    2    =    -28

     -20    +    3    =    -17

     -15    +    4    =    -11    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -15  and  4

                    6n2 - 15n + 4n - 10

Step-4 : Add up the first 2 terms, pulling out like factors :

                   3n • (2n-5)

             Add up the last 2 terms, pulling out common factors :

                   2 • (2n-5)

Step-5 : Add up the four terms of step 4 :

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            Which is the desired factorization

Final result :

 (2n - 5) • (3n + 2)

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