Find the vertices, foci, eccentricity and length of the latus rectum of the ellipse whose equation is x^2 + 9Y^2 = 9

Answer 1

divide by 9

x^2/(1/9) + y^2 = 1
a^2 = 1/9, a = ±1/3
b = ±1

so we have an ellipse with the major axis as the y-axis
vertices:
on x-axis ( 1/3,0) , (-1/3 , 0)
on y-axis (0,1) , (0,-1)

foci:
c^2 + (1/3)^2 = 1^1
c^2 = 1-1/9 = 8/9
c= ± (2√2)/3
this will give you the foci

e =c/b= (2√2/3)/1 = (2/3)√2

Use your definition of latus rectum to finish the question.