(15)

Sol. Equation of a tangent to the given ellipse + = 1 ......(1)

can be chosen as y = mx + ......(2)

The coordinates of the intersection points of this tangent with the coordinate axes are

and

Length of the intercept made by the coordinate axes on the tangent is given by the equation

 2 = (a 2 m 2 + b 2 )

The value of m for which  is minimum (by calculus), is given by

= – (a 2 m 2 + b 2 ) + 2a 2 m = 0 ........(3)

⇒ – – + 2a 2 m + = 0

2m (a 2 – ) = 0 ⇒ m = 0, not possible

m 4 = ⇒ m 2 = +

Putting this value of m 2 in equation (3), gives the minimum value of  = a + b.

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