MathDB

In the x \minus{} y plane, let

l

be the tangent line at the point

A\left(\frac {a}{2},\ \frac {\sqrt {3}}{2}b\right)

on the ellipse \frac {x^2}{a^2} \plus{} \frac {y^2}{b^2}\equal{}1\ (0 < b < 1 < a). Let denote

S

be the area of the figure bounded by

l,

the

x

axis and the ellipse. (1) Find the equation of

l

. (2) Express

S

in terms of

a,\ b

. (3) Find the maximum value of

S

with the constraint a^2 \plus{} 3b^2 \equal{} 4.

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