The equation of a straight line passing through the point $(3, 6)$ and cutting the curve $y = \sqrt{x}$ orthogonally is

The sum of the intercepts made by a tangent drawn to the curve $\left(\frac{x}{a}\right)^n + \left(\frac{y}{b}\right)^n = 2$ at the point $(a, b)$ on the coordinate axes is:

The value of $c$ such that the straight line joining the points $(0,3)$ and $(5,-2)$ is tangent to the curve $y=\frac{c}{x+1}$ is

If $ST$ and $SN$ are the lengths of the subtangent and the subnormal at the point $\theta = \frac{\pi}{2}$ on the curve $x = a(\theta + \sin \theta ), y = a(1 - \cos \theta ), a \neq 0$,then:

The angle of intersection between the curves $y = 4x^2$ and $y = x^2$ is .......... $^o$.

The lengths of tangent, subtangent, normal and subnormal for the curve $y=x^2+x-1$ at $(1,1)$ are $A, B, C$ and $D$ respectively, then their increasing order is