ParabolaHard
Question
The parabolas y2 = 4x and x2 = 4y divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If S1, S2, S3 are respectively the areas of these parts numbered from top to bottom; then S1 : S2 : S3 is
Options
A.1 : 2 : 1
B.1 : 2 : 3
C.2 : 1 : 2
D.1 : 1 : 1
Solution
y2 = 4x and x2 = 4y are symmetric about line y = x
⇒ area bounded between y2 = 4x and y = x is
⇒ AS2 =
and AS1 = AS3 =
⇒ AS1 : AS2 : AS3 :: 1 : 1 : 1.
⇒ area bounded between y2 = 4x and y = x is
⇒ AS2 =
and AS1 = AS3 = ⇒ AS1 : AS2 : AS3 :: 1 : 1 : 1.
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