Final answer:
An ellipse is a curved shape that is formed by the intersection of a cone and a plane. The major axis of an ellipse is the longest distance across the ellipse, while the minor axis is the shortest distance. In this question, we are given the coordinates of the foci (1,12) and (1,-6), and we are told that the major axis length is 30. To find the length of the major axis, we need to find the distance between the foci.
Step-by-step explanation:
An ellipse is a curved shape that is formed by the intersection of a cone and a plane. It has two foci, which are points inside the ellipse that help define its shape. The major axis of an ellipse is the longest distance across the ellipse, while the minor axis is the shortest distance.
In this question, we are given the coordinates of the foci (1,12) and (1,-6), and we are told that the major axis length is 30. To find the length of the major axis, we need to find the distance between the foci. Using the distance formula, we can calculate the distance between the two points:
Distance = sqrt((1-1)^2 + (12--6)^2) = sqrt((0)^2 + (18)^2) = sqrt(324) = 18
Since the major axis length is double the distance between the foci, the length of the major axis is 2 * 18 = 36.