The length of the subtangent at any point $(x_1, y_1)$ on the curve $y=5^x$ is

The values of parameter $a$ such that the line $(\log_{2}(1 + 5a - a^{2}))x - 5y - (a^{2} - 5) = 0$ is a normal to the curve $xy = 1$ may lie in the interval

The equation of the normal to the curve $xy + 7 = 0$ is $Ax + By + C = 0$. Which of the following is true?

The sum of the lengths of the subtangent and the subnormal drawn at $\theta = \frac{\pi}{3}$ on the cycloid $x = a(\theta - \sin \theta)$,$y = a(1 - \cos \theta)$ is

What is the equation of the tangent to the curve $y = 2 \sin x + \sin 2x$ at the point $x = \pi / 3$?

The abscissae of the points,where the tangent to the curve $y=x^{3}-3x^{2}-9x+5$ is parallel to the $x$-axis,are