If A ₁, ~A ₂, ~A ₃ are the areas of ellipse x^2+4 y^2-4=0 its director circle and auxiliary circle respectively, then A ₂+ A ₃- A ₁=

Step-by-step solution

aligned & x^2+4 y^2-4=0 & x^2 4 + y^2 1 =1, a^2=4, b^2=1 aligned Equation of director circle is x^2+y^2=a^2+b^2 x^2+y^2=5 Equation of Auxiliary circle is x^2+y^2=a^2 x^2+y^2=4 A ₁= Area of ellipse = a b=2 ₂= Area of Director circle =5 A ₃= Area of Auxiliary circle =4 So, A₂+A₃-A₁=5 +4 -2 =7