SOLUTION: Write an equation for an ellipse with its center at (2,3), one vertex at (6, 3), and one focus at (-1, 3). and Write an equation for a hyperbola with its center at (2, 3), on

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Write an equation for an ellipse with its center at (2,3), one vertex at (6, 3), and one focus at (-1, 3). and Write an equation for a hyperbola with its center at (2, 3), on      Log On


   

Question 875555: Write an equation for an ellipse with its center at (2,3), one vertex at (6, 3), and one focus at (-1, 3).
and
Write an equation for a hyperbola with its center at (2, 3), one vertex at (7, 3), and one focus at (14, 3).
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Ellipse: %28x-h%29%5E2%2Fa%5E2+%2B+%28y-k%29%5E2%2Fb%5E2+=+1+
where Pt(h,k) is the center. (a variable positioned to correspond with major axis)
a and b are the respective vertices distances from center
and ±sqrt%28a%5E2-b%5E2%29are the foci distances from center: a > b
center at (2,3), one vertex at (6, 3), a = (6-2) = 4
%28x-2%29%5E2%2F4%5E2+%2B+%28y-3%29%5E2%2Fb%5E2+=+1+
C(2,3)and one focus at (-1, 3). c = 3, 3^2 = (a^2 - b^2), 9 = 16 - b^2
%28x-2%29%5E2%2F16+%2B+%28y-3%29%5E2%2F7+=+1+