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What is the equation of the area of the ellipse when a cylinder of radius x is cut by a plane inclined at an angle a.

Angle a is the angle between the plane and the axis of the cylinder. If a is 90 then what we get is a circle of radius x.

PS. Consider the cylinder to be very long so that the plane cuts the cylinder completely

Any hints please?

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You can use some trigonometry to find the length of the major axis. A little thought should convince you that the length of the minor axis is $2x$. This is all the information you need to find the area.

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    $\begingroup$ (+1) Exactly. We get $A=\frac{\pi x^2}{\sin\alpha}$. $\endgroup$ – Jack D'Aurizio Dec 11 '14 at 0:57

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