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Mice21 [21]
2 years ago
15

Which is the equation of an ellipse with directrices at x = ±4 and foci at (2, 0) and (−2, 0)?

Mathematics
1 answer:
NemiM [27]2 years ago
6 0

Answer:

x squared over 4 plus y squared over 8 equals 1

Step-by-step explanation:

The general equation of ellipse is given as;

(x²/a²) + (y²/b²) = 1

The coordinates of a foci are: (±c, 0) where;

c² = b² - a²

However, we know that equation of directrix is; x = ±a/e

Now, Directrix is given ±4

Thus, a/e = 4

a = 4e

We also know that c = ae from ellipse foci coordinates.

Thus, ae = 2

since ae = 2, then (4e)e = 2

4e² = 2

e² = 2/4

e = 1/2

Thus;

a = 4 × 1/2

a = 2

Since c² = b² - a²;

2² = b² - 2²

4 = b² - 4

b² = 8

From (x²/a²) + (y²/b²) = 1, we can put our values to get;

x²/4 + y²/8 = 1

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Answer:

r = 7 cm; l = 11cm

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Step-by-step explanation:

(a) Radius of circle

The formula for the circumference of a circle is

A = 2πr

r = A/(2π)

Data:

C = 44 in

Calculation:

r = 44/(2 × 22/7)

   = 44/2 × 7/22

   =   2/2 × 7

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(b) Side of square

P = 4l

l =   P/4

  = 44/4

  = 11 in

(c) Areas

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A = πr²

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(ii) Square

A = l²

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  = 121 cm²

The circle encloses more area than the square.

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Step-by-step explanation:

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y = 2/3 x - 6

x = 2/3 y - 6

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Therefore , Mike took 1.882 hours to reach home .

8 0
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