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alex41 [277]
3 years ago
7

Write an equation for an ellipse centered at the origin, which has foci at ( 0 , ± 24 ) (0,±24)left parenthesis, 0, comma, plus

minus, 24, right parenthesis and co-vertices at ( ± 10 , 0 ) (±10,0)
Mathematics
1 answer:
alexandr402 [8]3 years ago
4 0

Answer:

\frac{x^{2}}{400} + \frac{y^{2}}{976} = 1

Step-by-step explanation:

The distance between foci with respect to origin is determined by mean of the Pythagorean Theorem:

2\cdot c = \sqrt{(0-0)^{2}+[24-(-24)]^{2}}

2\cdot c = 48

c = 24

The distance between origin and any of the horizontal co-vertices is:

a = \sqrt{[10-(-10)]^{2}+(0-0)^{2}}

a = 20

Now, the distance between origin and any of the vertical co-vertices is determined by the following Pythagorean relationship:

c^{2} = b^{2} - a^{2}

b^{2} = a^{2} + c^{2}

b = \sqrt{a^{2}+c^{2}}

b = \sqrt{20^{2}+ 24^{2}}

b = 4\sqrt{61}

Lastly, the equation of the ellipse in standard form is:

\frac{x^{2}}{400} + \frac{y^{2}}{976} = 1

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