If the lengths of semi-major and semi-minor axes of an ellipse are 2 and 3 and their corresponding equations are y - 5 = 0 and x + 3 = 0 , then write the equation of the ellipse.

The lengths of the semi major and the semi minor axes of the ellipse are 2 and 3 , respectively. Their corresponding equations are y - 5 = 0 and x + 3 = 0 So a = 2 and b = 3 The equation of the ellipse is given by ( x + 3 ) 2 4 + ( y - 5 ) 2 3 = 1 ⇒ 3 ( x + 3 ) 2 + 4 ( y - 5 ) 2 = 12 ⇒ 3 x 2 + 9 + 6 x + 4 y 2 + 25 - 10 y = 12 ⇒ 3 x 2 + 27 + 18 x + 4 y 2 + 100 - 40 y = 12 ⇒ 3 x 2 + 4 y 2 + 18 x - 40 y + 115 = 0

If the lengths of semi-major and semi-minor axes of an ellipse are 2 and 3 and their corresponding equations are y - 5 = 0 and x + 3 = 0 , then write the equation of the ellipse.

The lengths of the semi major and the semi minor axes of the ellipse are 2 and 3 , respectively. Their corresponding equations are y - 5 = 0 and x + 3 = 0 So a = 2 and b = 3 The equation of the ellipse is given by ( x + 3 ) 2 4 + ( y - 5 ) 2 3 = 1 ⇒ 3 ( x + 3 ) 2 + 4 ( y - 5 ) 2 = 12 ⇒ 3 x 2 + 9 + 6 x + 4 y 2 + 25 - 10 y = 12 ⇒ 3 x 2 + 27 + 18 x + 4 y 2 + 100 - 40 y = 12 ⇒ 3 x 2 + 4 y 2 + 18 x - 40 y + 115 = 0