Write the equation of an ellipse centered at the origin with height 8 units and width 16 units. Be sure to show or explain how you got your answer
The standard equation for an ellipse centered at the origin is:
(x^2/a^2) + (y^2/b^2) = 1
where "a" is the semi-major axis (half the width) and "b" is the semi-minor axis (half the height).
In this case, the height is 8 units and the width is 16 units, so:
a = 16/2 = 8
b = 8/2 = 4
Substituting these values into the standard equation gives:
(x^2/8^2) + (y^2/4^2) = 1
Simplifying, we get:
(x^2/64) + (y^2/16) = 1
Therefore, the equation of the ellipse centered at the origin with height 8 units and width 16 units is:
(x^2/64) + (y^2/16) = 1
To write the equation of an ellipse centered at the origin with a height of 8 units and a width of 16 units, we can use the standard form of an ellipse equation:
(x^2/a^2) + (y^2/b^2) = 1
where 'a' represents the half of the width (also known as the semi-major axis) and 'b' represents the half of the height (also known as the semi-minor axis).
In this case, since the width is 16 units, the value of 'a' is half of that, which is 8 units. Similarly, since the height is 8 units, 'b' is half of that, which is also 4 units.
Plugging these values into the equation, we get:
(x^2/8^2) + (y^2/4^2) = 1
Simplifying further, we have:
(x^2/64) + (y^2/16) = 1
Thus, the equation of the ellipse centered at the origin with a height of 8 units and a width of 16 units is:
x^2/64 + y^2/16 = 1
To find the equation of an ellipse centered at the origin, we need to know the semi-major axis (a) and the semi-minor axis (b). The semi-major axis represents the radius of the ellipse in the horizontal direction, while the semi-minor axis represents the radius of the ellipse in the vertical direction.
In this case, we are given the height of the ellipse as 8 units, which corresponds to the semi-minor axis (b), and the width of the ellipse as 16 units, which corresponds to the semi-major axis (a).
The equation of an ellipse centered at the origin is:
(x^2 / a^2) + (y^2 / b^2) = 1
Plugging in the values for a and b, we get:
(x^2 / 16^2) + (y^2 / 8^2) = 1
Simplifying further, we have:
(x^2 / 256) + (y^2 / 64) = 1
Therefore, the equation of the ellipse centered at the origin with height 8 units and width 16 units is (x^2 / 256) + (y^2 / 64) = 1.