Help me with my math?

Question

the perimeter of a triangle is 20 and the points

(2;-3) and (2;3) are two of the vertices...find the equation of the graph

which gives the possible location of the third vertex

use ellipse formula to solve

pls...show the solution

Answer 1

the distance between (2,3) and (2,-3) is 6 so the sum of the other sides is 14.

So the other vertex is on a ellipse with focus (2,3) (2,-3) and 2a=14

The center is(2,0) and 2c = 6

Taking  a coordinate system with origin a that point the equation of the ellipse is as b^2= 49-9=40

X^2/40 +Y^2/49=1(observe that the focal axis is OY)

Returning to the original system as

X=x-2 and Y=y

(x-2)^2/40 +y^2/49=1