The equation of the tangent to the curve $(1+x^2)y = 2-x$,where it crosses the $X$-axis,is

The length of the subtangent at $(2, 2)$ to the curve $x^5 = 2y^4$ 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 tangent to the curve $y = e^x$ at the point $(c, e^c)$ intersects the line joining the points $(c - 1, e^{c-1})$ and $(c + 1, e^{c+1})$ at a point whose $x$-coordinate is:

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

If the tangent drawn at a point $P$ on the curve $y=3x^2-5x+7$ is parallel to its chord joining the points $(1, y_1)$ and $(2, y_2)$ on it,then the $x$-coordinate of the point $P$ is