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

If the line $x + By + C = 0$ is the normal to the curve given by $x = a \sin^3 t$ and $y = b \cos^3 t$ (where $a, b \neq 0$) at the point $t = \frac{\pi}{2}$, then $B - C =$

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 length of the subtangent at any point $(x_1, y_1)$ on the curve $y=5^x$ is

The length of the subtangent at $(2, 2)$ to the curve $x^5 = 2y^4$ is

Let $m$ be the slope of the normal $L$ drawn at $(1, 2)$ to the curve $x = t^2 - 7t + 7, y = t^2 - 4t - 10$ and $ax + by + c = 0$ be the equation of the normal $L$. If the $G$.$C$.$D$. of $(a, b, c)$ is $1$, then $m(a + b + c) =$