elipses 2

Question

Find an equation in standard form for the ellipse with the vertical major axis of length 18, and minor axis of length 16.

Answer 1

The standardform of ellipse( x - h )²/b ² + ( y - k )²/a ² = 1 , if a ² > b ² .

If the larger denominator is under the "y " term, then the ellipse is vertical with center (h, k ) and

a = length of vertical - major axis and b  = length of vertical - minor axis.

Length of vertical - major axis = 2a = 18 ⇒ a = 9 ,

Length of vertical - minor axis = 2b = 16 ⇒ b = 8, and

Considering the center of the ellipse as C(h, k ) = (0, 0).

Plug those values into the standard form of the ellipse equation.

(x - 0 )²/ 8² + (y - 0 )²  /   9² = 1

x ²/ 64 + y ²/ 81 = 1.

Therefore, the equation of the ellipse in standard form is x ²/ 64 + y ²/ 81 = 1.