The angle between the tangents to the curve $y = x^2 - 5x + 6$ at the points $(2, 0)$ and $(3, 0)$ is:

The equation of the normal to the curve $y^4=a x^3$ at $(a, a)$ is

Consider $f(x) = \tan^{-1}\left(\sqrt{\frac{1 + \sin x}{1 - \sin x}}\right)$,where $x \in (0, \frac{\pi}{2})$. $A$ normal to $y = f(x)$ at $x = \frac{\pi}{6}$ also passes through the point:

An angle between the curves $x^2=3y$ and $x^2+y^2=4$ is

For any point on a curve,what is $\sqrt{\frac{\text{subnormal}}{\text{subtangent}}}$ equal to?

Let $f(x)$ be a differentiable function,$A(0, \alpha)$ and $B(8, \beta)$ be two points on the curve $y=f(x)$. Given $f(0)=2$ and $f^{\prime}(4)=\frac{-3}{4}$. If the chord $AB$ of the curve is parallel to the tangent drawn at the point $(4, f(4))$,then $\beta=$