The tangent to the curve $y=e^x$ drawn at the point $(c, e^c)$ intersects the line joining the points $(c-1, e^{c-1})$ and $(c+1, e^{c+1})$:

Find the coordinates of the point on the curve $\sqrt{x}+\sqrt{y}=4$ at which the tangent is equally inclined to the axes.

$A$ curve is represented by the equations $x = \sec^2 t$ and $y = \cot t$,where $t$ is a parameter. If the tangent at the point $P$ on the curve where $t = \pi/4$ meets the curve again at the point $Q$,then the $x$-coordinate of $Q$ is equal to

The number of those tangents to the curve $y^2 - 2x^3 - 4y + 8 = 0$ which pass through the point $(1, 2)$ is

The equation of the tangent to the curve $\sqrt{x} + \sqrt{y} = \sqrt{a}$ at the point $(x_1, y_1)$ is:

If $y=4x-5$ is a tangent to the curve $y^2=px^3+q$ at $(2,3)$,then $p-q$ is