What is the area enclosed by the curve `2x^(2) + y^(2) = 1` ?

Options

A. `2pi`
B. `pi`
C. `pi/2`
D. `(pi)/(sqrt(2))`

Answer

D

Explanation

Given equation of curve `2x^(2) + y^(2) = 1` is an ellipse which can be written as `(x^(2))/(y^(2))+(y^(2))/(1) = 1`.
Area of ellipse `(x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1` is `A = pi ab sq` unit
Here , `a = 1/(sqrt(2)), b = 1`.
`:.` Required area `= pi.(1)/(sqrt(2)).1 = (pi)/(sqrt(2)) sq` units.