Area under the curveHard

Question

Let f(x) = x2 + 6x + 1 and R denote the set of points (x, y) in the coordinate plane such that f(x) + f(y) ≤ 0 and f(x) - f(y) ≤ 0. The area of R is equal to -

Options

A.16π
B.12π
C.8π
D.4π

Solution

     
x2 + y2 + 6(x + y) + 2 ≤ 0
& x2 - y2 + 6(x - y) ≤ 0
⇒ (x - y)(x + y + 6) ≤ 0
from this we get a circle is two straight line which are at right angle
area = 2 quarter half circle =

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