Show that `x^(2) - y^(2) = a^(2) an dxy = c^(2)` cut orthogonally

If 4x^(2)+ py^(2) =45 and x^(2)-4y^(2) =5 cut orthogonally, then the value of p is

Show that the two curves x^(2)-y^(2)=r^(2) and xy=c^(2) where c,r are constants, cut orthogonally.

The curves 2x^(2) + 3y^(2) = 1 and cx^(2) + 4y^(2) = 1 cut each other orthogonally then the value of c is:

The curves 4x^2+9y^2=72 and x^2-y^2=5a t(3,2) touch each other (b) cut orthogonally intersect at 45^0 (d) intersect at 60^0

The curves 4x^2+9y^2=72 and x^2-y^2=5a t(3,2) touch each other (b) cut orthogonally intersect at 45^0 (d) intersect at 60^0

Show that f (x,y) = (2x ^(2) -y ^(2))/sqrt(x ^(2) + y ^(2)) is a homogeneous function of degree 1.

If the curves ax^(2) + by^(2) =1 and a_(1) x^(2) + b_(1) y^(2) = 1 intersect each other orthogonally then show that (1)/(a) - (1)/(b) = (1)/(a_(1)) - (1)/(b_(1))

The two curves x^3-3xy^2+2=0 and 3x^2y-y^3-2=0 cuts orthogonally

If 4(x-sqrt2)^(2)-lambda(y-sqrt3)^(2)=45 and (x-sqrt2)^(2)-4(y-sqrt3)^(2)=5 cut orthogonally, then integral value of lambda is ________.