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Chapter 10: Q. 12 (page 654)

If the foci of an ellipse are (-4,4)and(6,4), then the coordinates of the center of the ellipse are _____ .

Short Answer

Expert verified

If the foci of an ellipse are (-4,4)and(6,4), then the coordinates of the center of the ellipse are role="math" localid="1646847484430" (1,4) .

Step by step solution

01

Step 1. Given Information

We want to fill the gap in the given equation with the missing terms.

We know that

Property of ellipse: In any ellipse, its center is the mid-point between the two foci and located on the major axis.

02

Step 2. Method to solve:

We are going to sue the following formula to determine the midpoint of the two given points.

If the given points are (x1,y1)and(x2,y2)then their midpoint is:x1+x22,y1+y22

03

Step 4. Finding the center:

Plug in (x1,y1)=(-4,4)and(x2,y2)=(6,4)in the previous formula

-4+62,4+42=22,82=1,4

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