$y=x^2$ is the given curve. Imagine that this curve is dragged along the positive $X$-axis to a distance of ' $a$ ' units. If the acute angle between the curves at two positions is $\theta$, then

If $x$ and $y$ are two positive integers such that $x+2 y=10$ and $x^2 y^3$ is maximum, then $x^2+2 y^3=$

The equation of the normal to the curve $\sin y=\sqrt{3} x \sin \left(\frac{\pi}{6}+y\right)$ at $x=0$, is

Assertion (A) The curves $y^2=4 x$ and $x^2=-2 y$ intersect at $(1,2)$ orthogonally.

Reason (R) If the product of the slopes of the tangents drawn to two curves at their point of intersection is -1 , then the curves are said to cut each other orthogonally.