The equation of the tangent to the curve $y^{2}=ax^{2}+b$ at the point $(2,3)$ is $y=4x-5$. Then the values of $a$ and $b$ are:

The tangent to a non-linear curve $y = f(x)$ at any point $P(x, y)$ intersects the $x$-axis and $y$-axis at $A$ and $B$ respectively. If the normal to the curve $y = f(x)$ at $P$ intersects the $y$-axis at $C$ such that $AC = BC$,and $f(2) = 3$,then the equation of the curve is:

If the slope of the tangent to the curve $y=ax^3+bx+4$ at the point $(2, 14)$ is $21$,then the values of $a$ and $b$ are respectively:

The length of the segment of the tangent line to the curve $x=a \cos ^3 t, y=a \sin ^3 t$,at any point on the curve cut off by the coordinate axes is

The equation of the tangent to the curve $y=1-e^{\frac{x}{3}}$ at the point of intersection with the $Y$-axis is

The length of the normal at point $t$ of the curve $x = a(t + \sin t)$,$y = a(1 - \cos t)$ is