RD Sharma - Mathematics (Volume 2)

Book: RD Sharma - Mathematics (Volume 2)

Chapter: 21. Areas of Bounded Regions

Subject: Maths - Class 12th

Q. No. 29 of MCQ

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29

The area of the circle x2 + y2 = 16 enterior to the parabola y2 = 6x is

The area we want is –



At intersection points, y2 = 6x = 16 – x2


Or, x2 + 6x – 16 = 0


i.e., (x + 8)(x – 2) = 0


i.e., x = -8, 2


Now x = -8 y2 = 16 – (-8)2 = 16 – 64 = -48 < 0, which is not possible for y


So, x = 2


and y2 = 16 – 22


= 16 – 4


= 12


Or, y = √12 = ± 2√3


So, our bounds are y = -2√3 to y = 2√3


The area A enclosed is –


A =


Since both the functions are symmetrical about the x – axis,


A =


=





(Ans)

1

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