Question

The area of the region bounded by the ellipse = 1 and the ordinates x = ±ae where b² = a² (1 – e²) and e < 1, is given by –

• A. 2ab (e$\sqrt { 1 - \mathrm { e } ^ { 2 } }$+ sin^–1 e) sq. units
• B. 2ab (e$\sqrt { 1 - \mathrm { e } ^ { 2 } }$– sin^–1 e) sq. units
• C. ab (e$\sqrt { 1 - \mathrm { e } ^ { 2 } }$– sin^–1 e) sq. units
• D. None of these

Answer 1

Answer: (A)

2ab (e$\sqrt { 1 - \mathrm { e } ^ { 2 } }$+ sin^–1 e) sq. units

Answer 2

The required area

= dx =

=

= [ae + a² sin^–1 e]

= 2ab (e $\sqrt { 1 - \mathrm { e } ^ { 2 } }$+ sin^–1 e) sq. units.