Question

Help please! The question is tagged in the picture below!

Answer 1

General equation for vertical ellipse: (major axis is vertical axis)

`(y^2)/(a^2) + (x^2)/(b^2) = 1`

You are given that vertical height is 50 along major axis.
Therefore, a = 50.

To solve for 'b' use given point (30,12)


`(12^2)/(50^2) + (30^2)/(b^2) = 1 \\ \\ (30^2)/(b^2) = (50^2 - 12^2)/(50^2) \\ \\ (b^2)/(30^2) = (50^2)/(50^2-12^2) \\ \\ b^2 = (2250000)/(2356)`

Final ellipse equation:

`(y^2)/(2500) + (2356 x^2)/(2250000) = 1`