Rotate the ellipse to meet the parabola

Geometry Level pending

The ellipse

x 2 7 2 + y 2 3 2 = 1 \dfrac{x^2}{7^2}+ \dfrac{y^2}{3^2} = 1

is shifted to the right such that its left focus becomes at the origin. Then, the ellipse is rotated, about the origin, counter clockwise by an angle θ , 0 θ < 36 0 , \theta , 0^{\circ} \le \theta \lt 360^{\circ} , so that it becomes tangent to the parabola y = 5 + 1 16 ( x 12 ) 2 y = 5 + \dfrac{1}{16} (x - 12)^2 . Find the angle of rotation θ \theta in degrees (choose the smaller of two possible angles), and submit 100 θ \lfloor 100 \hspace{4pt} \theta \rfloor .


The answer is 1616.

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