write an equation of an ellipse:
Major axis 12 units long and parallel to the y-axis,
Minor axis 8 units long, center at (-2,5)
Surely somewhere in your text there is a highlighted box which states something like:
the formula for an ellipse with semi-major axis a and semi-minor axis b, centered at (h,k) is
(x-h)^2/a^2 + (y-k)^2/b^2 = 1 if a>b
Here, we have b>a, so
(x+2)^2/4^2 + (y-5)^2/6^2 = 1
(x+2)^2/16 + (y-5)^2/36 = 1
the equation i got since im doing conic sections, via ellipises is
(y-5)^2/36+(x+2)^2/16=1
To write the equation of an ellipse with the given properties, we can use the standard form of the equation for an ellipse:
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1
where (h, k) represents the center of the ellipse, and a and b represent the lengths of the semi-major and semi-minor axes, respectively.
Given the information provided, we have:
Center: (h, k) = (-2, 5)
Length of semi-major axis: a = 12/2 = 6 (since the major axis is 12 units, the semi-major axis is half that length)
Length of semi-minor axis: b = 8/2 = 4 (since the minor axis is 8 units, the semi-minor axis is half that length)
Substituting these values into the general equation of an ellipse, we get:
(x + 2)^2 / 6^2 + (y - 5)^2 / 4^2 = 1
Simplifying the equation further, we have:
(x + 2)^2 / 36 + (y - 5)^2 / 16 = 1
Thus, the equation of the ellipse is (x + 2)^2 / 36 + (y - 5)^2 / 16 = 1.
To write the equation of an ellipse, we need some information about its major and minor axes, as well as the position of its center. The general equation for an ellipse in standard form is:
((x-h)^2)/(a^2) + ((y-k)^2)/(b^2) = 1
where (h, k) represents the center of the ellipse, and 'a' and 'b' are the semi-major and semi-minor axes, respectively.
In this case, the major axis is parallel to the y-axis and 12 units long, while the minor axis is 8 units long and the center is at (-2, 5).
Let's find the values for 'h', 'k', 'a', and 'b':
The center of the ellipse is given as (-2, 5), so h = -2 and k = 5.
The semi-major axis 'a' is half the length of the major axis, so a = 12/2 = 6.
The semi-minor axis 'b' is half the length of the minor axis, so b = 8/2 = 4.
Now we can substitute these values into the equation:
((x - (-2))^2)/(6^2) + ((y - 5)^2)/(4^2) = 1
Simplifying and squaring the terms:
(x + 2)^2/36 + (y - 5)^2/16 = 1
Therefore, the equation of the ellipse with a major axis 12 units long and parallel to the y-axis, a minor axis 8 units long, and a center at (-2, 5) is ((x + 2)^2)/36 + ((y - 5)^2)/16 = 1.