JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(P_{1}:y=4x^{2}\) and \(P_{2}:y=x^{2}+27\) be two parabolas. If the area of the bounded region enclosed between \(P_{1}\) and \(P_{2}\) is six times the area of the bounded region enclosed between the line \(y=\alpha x, \alpha>0\) and \(P_{1},\) then \(\alpha\) is equal to :
- A 8
- B 15
- C 12
- D 6
Answer & Solution
Correct Answer
(C) 12
Step-by-step Solution
Detailed explanation
Area bounded between \(P_{1}\&P_{2}\) is \(\int_{-3}^3\left(\left(x^2+27\right)-\left(4 x^2\right)\right) d x\) \(\left(\right.\)P.O.I. of \(P_1 \& P_2\) is \(\left.x= \pm 3\right)\) \(=2 \int_0^3\left(27-3 x^2\right) d x=2\left[27 x-x^3\right]_0^3\) \(=2[81-27]=108\)…
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