Statement -1 : The area enclosed between the parabolas $y^{2} - 2 y + 4 x + 5 = 0$ and $x^{2} + 2 x - y + 2 = 0$ is same as that of bounded by curves $y^{2} = - 4 x$ and $x^{2} = y$ .
Statement – 2: Shifting of origin to point (h, k) does not change the bounded area

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If both the statements are TRUE and Statement-2 is the correct explanation of Statement-1.

If both the statements are TRUE and Statement-2 is NOT the correct explanation of Statement-1.

If Statement-1 is TRUE and Statement-2 is FALSE

If Statement-1 is FALSE and Statement-2 is TRUE

answer is A.

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Detailed Solution

Given curves are $y^{2} - 2 y + 4 x + 5 = 0 a n d x^{2} + 2 x - y + 2 = 0$ or ${(y - 1)}^{2} = - 4 (x + 1) a n d {(x + 1)}^{2} = y - 1$
Shifting origin to (-1, 1), equation of given curves changes to $y^{2} = - 4 x a n d X^{2} = Y$
Hence, statement -1 is true and statement-2 is correct explanation of statement -1.