The minimum radius vector of the curve a^2 x^2 + b^2 y^2 =1 is of length

Step-by-step solution

Given curve is a^2 x^2 + b^2 y^2 =1 Let radius vector is ' r ' array ll & r^2=x^2+y^2 r^2 & = a^2 y^2 y^2-b^2 +y^2 ( a^2 x^2 + b^2 y^2 =1 ) array For minimum value of r , aligned & & d (r^2 ) d y & =0 & & -2 y b^2 a^2 (y^2-b^2 )^2 +2 y & =0 & & y^2 & =b(a+b) & & x^2 & =a(a+b) & & r^2 & =(a+b)^2 & & r & =a+b aligned