If the major aixs is vertical and has a length of 10 units, the minor axis has a length of 8 units, and the Center C = (4,-2) fill in the missing denominators for the equation and determine the distance from C to the foci.
(x-4)^2 + (y+2)^2 = 1, distance from C to foci
Notice that the operation between the (x-4)^2 and (y+2)^2 is addition, which indicates that the figure is an ellipse.
Since it is an ellipse and has a vertical major axis, to complete the equation, apply the formula:
where a is the length of semi-major axis and b is the length of semi-minor axis.
So to get the value of a, take half of the length of major axis which is 10.
And to determine b, take half the length of minor axis which is 8.
Then, plug-in these values of a and b to the formula.
`(x-4)^2/4^2 + (y+2)^2/5^2=1`
Hence, the complete equation is `(x-4)^2/16+(y+2)^2/25=1` .
Next, to determine the distance of the focus from the center, apply the formula:
Plug-in a=5 and b=4.
Hence, the distance of each focus from the center C is 3 units.