Write an equation for an ellipse centered at the origin, which has foci at (+-sqrt8,0) and co-vertices at (0,+-sqrt10).

Given Information: We are given the foci at (±√8, 0) and co-vertices at (0, ±√10). The center of the ellipse is at the origin (0, 0). To write the equation of the ellipse in standard form, we need to find the values of a, b, and c, where a is the semi-major axis, b is the semi-minor axis, and c is the distance from the center to a focus.Finding the Value of c: The distance from the center to a focus, c, is given as √8. Therefore, c = √8.Finding the Value of b: The length of the semi-minor axis, b, is given by the distance from the center to a co-vertex. Since the co-vertices are at (0, ±√10), b = √10.Finding the Value of a: To find the length of the semi-major axis, a, we use the relationship c² = a² - b², which comes from the definition of an ellipse. We already know c and b, so we can solve for a. c² = a² - b² (√8)² = a² - (√10)² 8 = a² - 10 a² = 8 + 10 a² = 18 a = √18 a = 3√2Writing the Equation in Standard Form: Now that we have a, b, and c, we can write the equation of the ellipse in standard form. The standard form of an ellipse with a horizontal major axis is (x²/a²) + (y²/b²) = 1.Substitute the values of a and b into the standard form equation of the ellipse: (x²/a²) + (y²/b²) = 1 (x²/(3√2)²) + (y²/(√10)²) = 1 (x²/18) + (y²/10) = 1

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Write an equation for an ellipse centered at the origin, which has foci at
(+-sqrt8,0) and co-vertices at
(0,+-sqrt10).

Write an equation for an ellipse centered at the origin, which has foci at $( \pm \sqrt{8}, 0)$ and co-vertices at $(0, \pm \sqrt{10})$ .

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Algebra 2

Write equations of ellipses in standard form using properties

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Q. Write an equation for an ellipse centered at the origin, which has foci at

( \pm \sqrt{8}, 0)

and co-vertices at

(0, \pm \sqrt{10})

Given Information: We are given the foci at $(\pm\sqrt{8}, 0)$ and co-vertices at $(0, \pm\sqrt{10})$ . The center of the ellipse is at the origin $(0, 0)$ . To write the equation of the ellipse in standard form, we need to find the values of $a$ , $b$ , and $c$ , where $a$ is the semi-major axis, $b$ is the semi-minor axis, and $c$ is the distance from the center to a focus.
Finding the Value of $c$ : The distance from the center to a focus, $c$ , is given as $\sqrt{8}$ . Therefore, $c = \sqrt{8}$ .
Finding the Value of $b$ : The length of the semi-minor axis, $b$ , is given by the distance from the center to a co-vertex. Since the co-vertices are at $(0, \pm\sqrt{10})$ , $b = \sqrt{10}$ .
Finding the Value of a: To find the length of the semi-major axis, $a$ , we use the relationship $c^2 = a^2 - b^2$ , which comes from the definition of an ellipse. We already know $c$ and $b$ , so we can solve for $a$ .
$c^2 = a^2 - b^2$
$(\sqrt{8})^2 = a^2 - (\sqrt{10})^2$
$8 = a^2 - 10$
$a^2 = 8 + 10$
$a^2 = 18$
$c^2 = a^2 - b^2$ $0$
$c^2 = a^2 - b^2$ $1$
Writing the Equation in Standard Form: Now that we have $a$ , $b$ , and $c$ , we can write the equation of the ellipse in standard form. The standard form of an ellipse with a horizontal major axis is $(x^2/a^2) + (y^2/b^2) = 1$ .
Writing the Equation in Standard Form: Now that we have $a$ , $b$ , and $c$ , we can write the equation of the ellipse in standard form. The standard form of an ellipse with a horizontal major axis is $(x^2/a^2) + (y^2/b^2) = 1$ .Substitute the values of $a$ and $b$ into the standard form equation of the ellipse: $\newline$ $(x^2/a^2) + (y^2/b^2) = 1$ $\newline$ $(x^2/(3\sqrt{2})^2) + (y^2/(\sqrt{10})^2) = 1$ $\newline$ $(x^2/18) + (y^2/10) = 1$