Question

Write the standard form equation of the ellipse with vertices (-5,4) and (8,4) and whose focus is (-4,4)

Answer 1

Step 1:

Vertices : .

Focus is  : .

Since the -coordinates of the vertices, it is a horizontal ellipse.

Mid point of the vertices is centre of the ellipse.

If are vertices of the ellipse then their midpoint is the centre of the ellipse.

Find the mid point of the points .

.

Center of the ellipse is .

Step 2:

Distance from the center to vertex is .

Distance between the two points and is .

Find the distance from center to vertex .

.

Distance from the center to focus is .

Find the distance from center to focus .

.

Step 3:

The standard form of horizontal ellipse is , where .

For an ellipse .

Substitute and in .

.

Consider .

.

Substitute , and in the standard form of ellipse.

.

Solution:

The ellipse equation is .