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kolezko [41]
3 years ago
11

Which of the following is the standard equation of the ellipse with vertices at (1,0) and (27,0) and an eccentricity of 5/13?

Mathematics
1 answer:
Dovator [93]3 years ago
3 0

The equation of the elipse is given by:

\frac{(x - 14)^2}{169} + \frac{y^2}{144} = 1

The equation of an elipse of center (x_0, y_0) is given by:

\frac{(x - x_0)^2}{a^2} + \frac{(y - y_0)^2}{b^2} = 0

Values a and b are found according to the <u>vertices and the eccentricity</u>.

It has vertices at (1,0) and (27,0), thus:

x_0 = \frac{27 + 1}{2} = 14

y_0 = \frac{0 + 0}{2} = 0

a = \frac{27 - 1}{2} = 13

a^2 = 169

It has eccentricity of \frac{5}{13}, thus:

\frac{5}{13} = \frac{c}{a}

\frac{5}{13} = \frac{c}{13}

c = 13

Thus, b is given according to the following equation:

c^2 = a^2 - b^2

b^2 = a^2 - c^2

b^2 = 169 - 25

b = \sqrt{144}

b = 12

The equation of the elipse is:

\frac{(x - 14)^2}{169} + \frac{y^2}{144} = 1

A similar problem is given at brainly.com/question/21405803

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