Question

complete the sentence below.
if the center of an ellipse is (3, - 4), the major axis is parallel to the x - axis, and the distance from the center of the ellipse to its vertices is a = 5 units, then the coordinates of the vertices are

Explanation:

Step1: Determine the direction of major axis

Since the major axis is parallel to the \(x -\)axis, the vertices of the ellipse will be of the form \((h\pm a,k)\) where \((h,k)\) is the center of the ellipse.
Given the center \((h,k)=(3, - 4)\) and \(a = 5\) (distance from center to vertex).

Step2: Calculate the coordinates of vertices

Using the formula for vertices \((h\pm a,k)\)
For \(x\) - coordinate: \(h + a=3 + 5=8\) and \(h - a=3-5=-2\)
\(y\) - coordinate remains \(k=-4\)

Answer:

\((8,-4)\) and \((-2,-4)\)