For the curve `xy=c^(2)` the subnormal at any point varies as

For the curve y^(n)=a^(n-1)x if the subnormal at any point is a constant, then n is equal to

For the curve y^(n) -=a^(n-1)x if the subnormal at any point is a constant then n=

For the curve y=ax^(n) the length of the subnormal at any point is a constant. The value of n must be

The length of the normal to the curve y=a cos h (x/a) at any point varies as

The subnormal to the curve xy=c^2 at any point vaires directly as

The length of the normal to the curve y=a((e^(-x//a)+e^(x//a))/2) at any point varies as the

For the curve xy^(m)=a^(m+1) the length of the subnormal at any point is a constant. Then the value of m must be

Show that in the curve y=a log(x^(2)-a^(2)) the sum the lengths of the tangent and the subtangent at any point varies as the product of the coordinates of the point.

Show that at any point on the hyperbola xy=c^(2), the subtangent varies as the abscissa and the subnormal varies as the cube of the ordinate of the point of contact.