What is an equation is standard form of an ellipse centered at the origin with vertex (-5,0) and co-vertex (0,3)?
The standard form equation of an ellipse centered at the origin is:
(x^2/a^2) + (y^2/b^2) = 1
where a is the semi-major axis (distance from the center to the vertex) and b is the semi-minor axis (distance from the center to the co-vertex).
Since the ellipse is centered at the origin, the center is (0,0).
The vertex (-5,0) is 5 units to the left of the center, so a = 5.
The co-vertex (0,3) is 3 units above the center, so b = 3.
Substituting these values into the standard form equation, we get:
(x^2/25) + (y^2/9) = 1
Therefore, the equation in standard form of an ellipse centered at the origin with vertex (-5,0) and co-vertex (0,3) is (x^2/25) + (y^2/9) = 1.
are you sure
Yes, I am sure. The equation in standard form of an ellipse centered at the origin with vertex (-5,0) and co-vertex (0,3) is (x^2/25) + (y^2/9) = 1.
is that correct
Yes, that is correct.
To find the equation in standard form for an ellipse centered at the origin, we need to use the given vertex and co-vertex information.
The vertex of the ellipse is given as (-5, 0). This means that the distance from the center to the vertex along the x-axis is 5 units.
The co-vertex of the ellipse is given as (0, 3). This means that the distance from the center to the co-vertex along the y-axis is 3 units.
Using this information, we can determine the values of a and b, which represent the semi-major axis and semi-minor axis of the ellipse, respectively.
a = 5 (semi-major axis)
b = 3 (semi-minor axis)
The standard form equation for an ellipse centered at the origin is:
x^2/a^2 + y^2/b^2 = 1
Substituting the values of a and b:
x^2/5^2 + y^2/3^2 = 1
Simplifying the equation:
x^2/25 + y^2/9 = 1
Therefore, the equation in standard form for the ellipse centered at the origin with vertex (-5,0) and co-vertex (0,3) is:
x^2/25 + y^2/9 = 1
To find the equation of an ellipse in standard form, you need to know the coordinates of its center and the lengths of its major and minor axes.
In this case, the center of the ellipse is given as the origin (0, 0), which means that it is centered at (0, 0).
The vertex is given as (-5, 0), which means that the distance from the center to the vertex along the x-axis is 5 units. This gives us the length of the semi-major axis (a) of the ellipse.
The co-vertex is given as (0, 3), which means that the distance from the center to the co-vertex along the y-axis is 3 units. This gives us the length of the semi-minor axis (b) of the ellipse.
In standard form, the equation of an ellipse centered at the origin is:
(x^2 / a^2) + (y^2 / b^2) = 1
To find the values of a and b, we can use the lengths of the semi-major and semi-minor axes.
From the given information, we have a = 5 and b = 3.
Plugging these values into the equation, we get:
(x^2 / 5^2) + (y^2 / 3^2) = 1
Simplifying further:
(x^2 / 25) + (y^2 / 9) = 1
Therefore, the equation of the ellipse in standard form, centered at the origin, with vertex (-5, 0) and co-vertex (0, 3), is:
(x^2 / 25) + (y^2 / 9) = 1