General equation for vertical ellipse: (major axis is vertical axis)
[tex]\frac{y^2}{a^2} + \frac{x^2}{b^2} = 1[/tex]
You are given that vertical height is 50 along major axis.
Therefore, a = 50.
To solve for 'b' use given point (30,12)
[tex]\frac{12^2}{50^2} + \frac{30^2}{b^2} = 1 \\ \\ \frac{30^2}{b^2} = \frac{50^2 - 12^2}{50^2} \\ \\ \frac{b^2}{30^2} = \frac{50^2}{50^2-12^2} \\ \\ b^2 = \frac{2250000}{2356}[/tex]
Final ellipse equation:
[tex]\frac{y^2}{2500} + \frac{2356 x^2}{2250000} = 1[/tex]
