The point on the curve $y = 2 + \sqrt{4x + 1}$ at which the slope of the tangent is $\frac{2}{5}$ is:

What is the equation of the normal to the curve $y = x(2 - x)$ at the point $(2, 0)$?

The area of the triangle formed by the coordinate axes and a tangent to the curve $xy = a^2$ at the point $(x_1, y_1)$ is . . . . . . sq. units (where $a, x_1$,and $y_1$ are non-zero).

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

Let $f(x) = \begin{cases} -x^2 & \text{for } x < 0 \\ x^2 + 8 & \text{for } x \ge 0 \end{cases}$. Then the $x$-intercept of the line that is tangent to the graph of $f(x)$ is

If the length of the subnormal at any point on the curve $y = a^{1-n}x^n$ is constant,then $n = \dots$