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1326

Let b ≠ 0 and j = 0, 1, 2, .  .  . , n. Let Sj be the area of the region bounded by Y–axis and the curve
.

Show that S0, S1, S2, .  .  .  , Sn are in geometric progression. Also find the sum for a = − 1 and b = π.

a)

b)

c)

d)

Let b ≠ 0 and j = 0, 1, 2, .  .  . , n. Let Sj be the area of the region bounded by Y–axis and the curve
.

Show that S0, S1, S2, .  .  .  , Sn are in geometric progression. Also find the sum for a = − 1 and b = π.

a)

b)

c)

d)

IIT 2001
1327

A tangent to the ellipse x2 + 4y2 = 4 meets the ellipse x2 + 2y2 = 6 at P and Q. Prove that tangents at P and Q of the ellipse x2 + 2y2 = 6 are at right angles.

A tangent to the ellipse x2 + 4y2 = 4 meets the ellipse x2 + 2y2 = 6 at P and Q. Prove that tangents at P and Q of the ellipse x2 + 2y2 = 6 are at right angles.

 IIT 1997


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