Write an equation of an ellipse in standard form with the center at the origin and with the given characteristics.
vertex at (–5, 0) and co-vertex at (0, 4)
1. A
2. B
3. D
4. A
5. B
6. D
7. A
(x + 5)^2/25 + (y - 4)^2/16 = 1
the centre would be at (0,0) and a = 5, b = 4
my ellipse would be
x^2 / 25 + y^2 / 16 = 1
The robot's answer would have a centre at (-5, 4) and (-5,0) could NOT
be a vertex
tibb is 100% correct
Tibb is correct!
To write the equation of an ellipse in standard form, we need to determine the values for a, b, and c.
Let's start by identifying the center of the ellipse. We are given that the center is at the origin (0,0). The center of the ellipse is always represented as (h, k) in the standard form equation.
Since the center is at the origin, we have h = 0 and k = 0.
Next, we need to determine the values for a and b. The vertices of the ellipse are given as (–5, 0) and (0, 4). The distance from the origin to a vertex is called a, and the distance from the origin to a co-vertex is called b.
From the given information, we can determine that a = 5 and b = 4.
Finally, we can write the equation of the ellipse in standard form:
x^2/a^2 + y^2/b^2 = 1
Substituting the values for a and b, we have:
x^2/5^2 + y^2/4^2 = 1
Simplifying further, we get:
x^2/25 + y^2/16 = 1
Therefore, the equation of the ellipse in standard form with the given characteristics is: x^2/25 + y^2/16 = 1.