Find the equation of the ellipse given foci and length of major axis?

Question

Find an equation for the ellipse with foci at (0, -2) and (0, 2); length of the major axis is 8

Answer 1

The coordinates of foci are (0 , -2) and (0, 2)

Length of the major axis 2a = 8

a = 8/2 = 4

a² = 4² = 16

Centre is mid point of foci

Centre = ( Average of x-coordinates of foci ,  Average of y-coordinates of foci  )

Centre = ( (0+0)/2 , (-2+2/2) )

Centre (h , k) = ( 0 , 0 )

c = Distance from centre to foci

c = √[ (0-0)² + (0+2)² ]

c = √4 = 2

c² = a² - b²

b² = a² - c²

b² = 4² - 2² = 16 - 4

b² = 12

Th general form of  ellipse  : (x-h)²/a² + (y-k)²/b = 1

(x-0)²/16 + (y-0)²/12= 1

(x²/16) + (y²/12) = 1