The length of the subtangent at $(2, 2)$ to the curve $x^5 = 2y^4$ is

The length of the tangent to the curve $x = a(\cos t + \log \tan(t/2)), y = a \sin t$ is

The angle of intersection of curves $y = x^2$ and $6y = 7 - x^3$ at the point $(1, 1)$ is:

The curve $\left(\frac{x}{a}\right)^n+\left(\frac{y}{b}\right)^n=2$,where $n \in N$,touches the line at the point $(a, b)$. Find the equation of the line.

If the normal to the curve $y = f(x)$ at the point $(3, 4)$ makes an angle of $3\pi / 4$ with the positive $X$-axis,find $f'(3)$.

The subnormal at any point on the curve $xy^n = a^{n + 1}$ is constant for $n=$ ............