Find the standard form of the equation of an ellipse with center at (-2,1) with major axis length 10 along y axis and minor axis length 8 along the x axis
2a = 10 --->a=5
2b = 8 ---> b = 4
(x+2)^2 /25 + (y-1)^2 /16 = 1
46
To find the standard form equation of an ellipse, we can use the known properties of the ellipse - center, major and minor axis lengths. The standard form of the equation of an ellipse with center (h, k), major axis length 2a along the x-axis, and minor axis length 2b along the y-axis is:
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1
Given that the center of the ellipse is (-2, 1) and the major axis length is 10 along the y-axis (vertical) and the minor axis length is 8 along the x-axis (horizontal), we can fill in these values into the standard form equation.
Center (h, k) = (-2, 1)
Major axis length (2a) = 10
Minor axis length (2b) = 8
Using these values, we can calculate a and b:
a = major axis length / 2 = 10 / 2 = 5
b = minor axis length / 2 = 8 / 2 = 4
Now plugging in the calculated values, we get the standard form equation:
(x - (-2))^2 / 5^2 + (y - 1)^2 / 4^2 = 1
which simplifies to:
(x + 2)^2 / 25 + (y - 1)^2 / 16 = 1
Therefore, the standard form equation of the ellipse with center (-2, 1), major axis length 10 along the y-axis, and minor axis length 8 along the x-axis is:
(x + 2)^2 / 25 + (y - 1)^2 / 16 = 1