For y > 0, the given curve 2y^2 + x^2 = 64 is moved 5 units to the right. Find the point of intersection (x,y).
When we move this 5 units to the right, the function becomes
2y^2 + (x - 5)^2 = 64
Subtracting the given function from this gives us
(x - 5)^2 = x^2 simplify
x^2 -10x + 25 = x^2
-10x + 25
-10x = -25
x= -25/-10 = 2.5 = the x coordinate of the intersection
Andusing either equation to find y, we have
2y^2 + (2.5)^2 = 64
2y^2 + 6.25 = 64 subtract 6.25 from both sides
2y^2 = 57.75 divide both sides by 2
y^2 = 28.875 take the positive root
y = sqrt (28.875)
So ( x , y) = (2.5, sqrt (28.875) )
See the graph here : https://www.desmos.com/calculator/3lkazxxzgq