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3 years ago

An ellipse has vertex (0, 4), co-vertex (3, 0) and is centered at the origin. What is the equation for the ellipse?

Mathematics

1 answer:

yulyashka [42]3 years ago

5 0

Answer:

Step-by-step explanation:

Notice: The first vertex (0, 4) is further from the origin than is the second vertex (3, 0), in the y-direction and the x-direction, respectively.

The standard equation of an ellipse with center at the origin is

x² y²

------ + ------ = 1

a² b²

and a represents the greater distance from the origin to one covertex or the other. In this case we let a = 4 and b = 2. Then we have:

y² x²

---- + ------ = 1 which is the equation of this ellipse in final

4² 3² finished form.

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( 1 , -2 , 4 , -8 , 16 , ... )

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A geometric sequence has a common ratio in consecutive terms,

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$1, \frac{1}{2}, \frac{1}{6},\frac{1}{24},\frac{1}{120}.....$

$\frac{1/2}{1}\neq \frac{1/6}{1/2}\neq \frac{1/24}{1/6}\neq \frac{1/120}{1/24}...$

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1 , -2 , 3 , -4 , 5 , ...

$\frac{-2}{1}\neq \frac{3}{-2}\neq \frac{-4}{3}\neq \frac{5}{-4}...$

i.e. 1 , -2 , 3 , -4 , 5 , ... is not a Geometric sequence,

In sequence,

1 , -2 , 4 , -8 , 16 , ...

$\frac{-2}{1}=\frac{4}{-2}= \frac{-8}{4}= \frac{16}{-8}...$

i.e. 1 , -2 , 4 , -8 , 16 , .... is a Geometric sequence,

In sequence,

0 , 1 , 0 , -1 , 0 , .....

$\frac{1}{0}\neq \frac{0}{1}\neq \frac{-1}{0}\neq \frac{0}{-1}...$

i.e. 0 , 1 , 0 , -1 , 0 , .....is not a Geometric sequence,

In sequence,

9 , 3 , 1 , 1/3 , 1/9 , ...

$\frac{3}{9}=\frac{1}{3}= \frac{1/3}{1}= \frac{1/9}{1/3}...$

i.e. 9 , 3 , 1 , 1/3 , 1/9 , ... is a Geometric sequence,

In sequence,

1 , 3 , 5 , 7 , 9 , ...

$\frac{3}{1}\neq \frac{5}{3}\neq \frac{7}{5}\neq \frac{9}{7}...$

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