An ellipse has the equation x 629 y1249 1 a Is the major

An ellipse has the equation: (x - 6)^2/9 + (y+1)^2/49 = 1 a) Is the major axis horizontal or vertical? (b) Find the exact values of the foci of the ellipse. Show work.

Solution

(x-6)²/9 + (y+1)²/49= 1

If the larger denominator is under x term,its an horizontal ellipse and if the larger denominator is under y term,its a vertical ellipse.

Here the larger denominator is 49 which is under y term. So its a vertical ellipse.

The equation of ellipse is

(x-h)²/b² + (y-k)²/a²=1

Centre is (h,k)

a²=49 and b²=9

c= sqrt(a²-b²) = sqrt (49-9)=2sqrt10

Focii= (h,k+c),(h,k-c)

        = (6,-1+2sqrt10),(6,-1-2sqrt10)