The equation of the tangent to the curve $y=5x^2-3x+7$ at the point $(-1, 4)$ is:

Find the equation of all lines having slope $2$ which are tangents to the curve $y = \frac{1}{x-3}, x \neq 3$.

$x_1, x_2 \in N$. If a line having slope $2$ is a tangent to the curve $y=x^4-6x^3+13x^2-10x+5$ at points $P(x_1, y_1)$ and $Q(x_2, y_2)$,then $x_1x_2+y_1y_2=$

$p_1$ and $p_2$ are the perpendicular distances from the origin to the tangent and normal drawn at any point on the curve $x^{2/3} + y^{2/3} = a^{2/3}$ respectively. If $k_1 p_1^2 + k_2 p_2^2 = a^2$,then $k_1 + k_2 =$

What is the angle between the curves $y = \sin x$ and $y = \cos x$?

For the curve $\frac{x^n}{a^n}+\frac{y^n}{b^n}=2, (n \in N \text{ and } n > 1)$,the line $\frac{x}{a}+\frac{y}{b}=2$ is