The equation of the tangent to the curve $y=\sqrt{9-2x^2}$ at the point where the ordinate and abscissa are equal is

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:

The angle between the curves $y = \sin x$ and $y = \cos x$,$0 < x < \frac{\pi}{2}$,is

The equation of the tangent to the curve $x y^5+2 x^2 y-x^3+y+1=0$ at $x=0$ is

Let $a, b, c \in \mathbb{R}$ be such that $2a + 3b + 6c = 0$ and $g(x)$ be the antiderivative of $f(x) = ax^2 + bx + c$. If the slopes of the tangents drawn to the curve $y = g(x)$ at $(1, g(1))$ and $(2, g(2))$ are equal, then

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