Question

Area of the ellipse `x^2/9 + y^2/4` = 1 is ______.

Options

• 6π sq. units

• 3π sq. units

• `3/2`π sq. units

• 2π sq. units

Answer 1

Area of the ellipse `x^2/9 + y^2/4` = 1 is 6π sq. units.

Explanation:

Since the curve is symmetrical about Y-axis as well as X-axis.

∴ The area of the given ellipse

= 4(area of OABO)

= `4int_0^3 y"d"x`

= `4 int_0^3 2/3 sqrt(9 - x^2) "d"x`

= `8/3 int_0^(pi/2) 3cos theta*3costheta "d"theta`  ......[Put x = 3 sin θ]

= `24 int_0^(pi/2) ((1 + cos 2theta)/2)"d"theta`

= `12[[theta]_0^(pi/2) + [(sin 2theta)/2]_0^(pi/2)]`

= 6π sq. units