Find the minimum distance of origin from the curve `ax^(2) +2bxy+ay^(2)=c` where `a gt b gt c gt0`

The minimum distance from the origin to a point on the curve x^(2//3) +y^(2//3)=a^(2//3) (a gt 0 ) is

Find the points on the curve ax^(2)+2bxy+ay^(2)=c, 0ltaltbltc, whose distance from the origin is minimum.

Find the points on the curve ax^(2)+2bxy+ay^(2)=c, 0ltaltbltc, whose distance from the origin is minimum.

The area enclosed by the curves ax +- by +- c =0 where a, b, c gt 0

Find the minimum value of (a+1/a)^(2) +(b+1/b)^(2) where a gt 0, b gt 0 and a+b = sqrt(15)

Find the minimum value of (a+1/a)^(2) +(b+1/b)^(2) where a gt 0, b gt 0 and a+b = sqrt(15)