The area of the triangle formed by the tangent and the normal drawn to the curve $y^2=4 x$ at $(1,2)$ with $Y$-axis is (in square units)

Consider two families of curves $y^2=4 a x$ ( $a$ is a parameter) and $x^2+\frac{y^2}{2}=c^2(c$ is parameter). If one curve from each family is chosen, then the angle between those two curves is

Let a function $f(x)$ be continuous in an interval $[a, b]$. Let $\delta>0$ be a very small real number. Let $c \in(a, b)$ be such that $f(c-\delta)0$. Let $(f(\alpha-\delta)-f(\alpha))(f(\alpha+\delta))<0 \forall \alpha \in(a, b)$ and $\alpha \neq c$. Then,

If $\alpha$ is a root of multiplicity 3 of the equation $x^5-8 x^4+25 x^3-38 x^2+28 x-8=0$, then $\alpha^2-5 \alpha+6=$