If the curve `y^(2) = x and xy = k` are orthogonal then prove that `8k^(2) =1`

Prove that the curves x = y^(2) and xy = k cut at right angles* if 8k^(2) = 1 .

If the curves y=2e^(x)andy=ae^(-x) intersect orthogonally, then a = __________

If the curves a y+x^2=7a n dx^3=y cut orthogonally at (1,1) , then find the value adot

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

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))

Find the equations of the tangents to the curve y=1+x^(3) for which the tangent is orthogonal with the line x + 12y = 12.

Find the equation of the tangents to the curve y = 1 + x^(3) for which the tangent is orthogonal with the line x + 12y = 12 .

The locus of the center of a circle which cuts orthogonally the parabola y^2=4x at (1,2) is a curve

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