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Position of a Point W.R.T Hyperbola

If c>0 and th...

Question

If c>0 and the area of the region enclosed by the parabolas $y = x^{2} - c^{2}$ and $y = c^{2} - x^{2}$ is 576, then c =

A

6

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B

4

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C

3

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D

8

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Solution

The correct option is A 6
Area between the two parabolas = $4 \int_{0}^{c} (c^{2} - x^{2}) d x = \frac{8 c^{3}}{3} = 576$
only if c = 6

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