(x-2)^2/49+(y+1)^2/25=1

Question

i need help finding the foci, major axis, minor axis and verticies of this problem.

Answer 1

Given equation (x-2)^2/49 + (y+1)^2/25 = 1

(x-2)^2/7^2 + (y-(-1))^2/5^2 = 1

Compre it to ellipse equation (x-h)^2/a^2+(y-k)^2/b^2 = 1

a = 7, b = 5

→Major axis (a) = 7

→Minor axis (b) = 5

(h,k) = (2,-1)

→Vertices = (h±a,k)

(h+a,k) = (2+7,-1) = (9,-1)

(h-a,k) = (2-7,-1) = (-5,-1)

e = √(a^2-b^2)/a

e = √(49-25)/7 = 4.89/7 = 0.69

→Foci (h±ae,k)

(h+ae,k) = (2+7*0.69,-1) = (6.83,-1)

(h-ae,k) = (2-7*0.69,-1) = (-2.83,-1)