Prove that the curve `2x^2+3y^2=1 and x^2-y^2=1/12` intersect orthogonally.

Prove that the curve x^(2)+y^(2)+x+2y=0 and xy+2x-y=0 intersect orthogonally at the origin.

Prove that the curves x^(2)+y^(2)=ax and x^(2)+y^(2)=by are cuts orthogonally.

If the curves ax^2 + by^2 =1 and a'x^2 +b'y^2 =1 intersect orthogonally, prove that: 1/a-1/a'=1/b-1/b'

Prove that the curve y=x^(2) and xy=k intersect orthogonally if 8k^(2)=1

If the curves 2x^(2)+3y^(2)=6 and ax^(2)+4y^(2)=4 intersect orthogonally, then a =

If the curves 2x^(2)+3y^(2)=6 and ax^(2)+4y^(2)=4 intersect orthogonally, then a =

Prove that the curve y = x^2 and xy = k intersect orthogonally if 8k^2 = 1 .

If the curvs a x^2 + b y^2 = 1 and a' x^2 + b' y^2 =1 intersect orthogonally, then prove that frac{1}{a} - frac{1}{b} = frac{1}{a'} - frac{1}{b'}

If the curve ax^(2)+by^(2)=1 and a'x^(2)+b'y^(2)=1 intersect orthogonally, then