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Lelechka [254]
2 years ago
10

4. will give brainliest

Mathematics
1 answer:
saul85 [17]2 years ago
8 0

The equation of the ellipse in <em>standard</em> form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)

<h3>What is the equation of the ellipse associated with the coordinates of the foci?</h3>

By <em>analytical</em> geometry we know that foci are along the <em>major</em> axis of ellipses and beside the statement we find that such axis is parallel to the x-axis of Cartesian plane. Then, the <em>standard</em> form of the equation of the ellipse is of the following form:

(x - h)² / a² + (y - k)² / b² = 1, where a > b     (1)

Where:

  • a - Length of the major semiaxis.
  • b - Length of the minor semiaxis.

Now, we proceed to find the vertex and the lengths of the semiaxes:

a = 10 units.

b = 8 units.

Vertex

V(x, y) = 0.5 · F₁(x, y) + 0.5 · F₂(x, y)

V(x, y) = 0.5 · (3, 2) + 0.5 · (- 9, 2)

V(x, y) = (1.5, 1) + (- 4.5, 1)

V(x, y) = (- 3, 2)

The equation of the ellipse in <em>standard</em> form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)

To learn more on ellipses: brainly.com/question/14281133

#SPJ1

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