[tex] 14 x^{2} +4 y^{2} = 196
[/tex][tex] \frac{14 x^{2} }{196} + \frac{4y}{196} = 1
[/tex]
[tex] \frac{ x^{2} }{14} + \frac{ y^{2} }{49} = 1
To find Major Axis we have to find biggest denominator, it is 49.
The major axis is on the y-axis.
49=a^2, a=7,
Center (0,0).
Vertices of major axis =(0,0+a) and (0,0-a)
Vertices of major axis(0,-7), (0,+7)
Minor axis is on the x-axis.
b^2=14, b= \sqrt{14}
Vertices of minor axis (- \sqrt{14}, 0), ( \sqrt{14} , 0)
[/tex]
