Question

write an equation for a set of points in the plane such that the sum of the distances from (-7,0) and (7,0) is 20

Answer 1

This is the definition of an ellipse, right?

Answer 2

Oh, I see that the asker is not present.

Answer 3

I think so

Answer 4

So by definition, 2a = 20. You can find the center because it is half way between the focal points.

Answer 5

yes that I have done

Answer 6

from here is where I am lost

Answer 7

What is c?

Answer 8

im not sure

Answer 9

What is the center?

Answer 10

well 0

Answer 11

The center has an x and a y coordinate.

Answer 12

yes wouldn't it be (0,0)?

Answer 13

It is (0,0) And c is the distance from the center to the foci so c = 7. 2a=20 so a = 10
a^2-b^2=c^2 so 100-b^2=49 and b^2= 51. So now you know the center, a^2 and b^2. You can write the equation.

Answer 14

ok thanks

Answer 15

yw

Answer 16

so its (x+7)^2/51 + (y-0)^2/100=1

Answer 17

a^2 goes under x^2 when the major axis is horizontal.