The length of the subnormal to any point on a curve is always constant. Then,the curve is . . . . . . .

The number of points on the curve $y=2t^2+3t-5$ and $x=t^3-4t^2-3t$ such that the normals drawn at them on the curve are parallel to the $X$-axis is

Length of the subtangent at $(x_{1}, y_{1})$ on $x^{n} y^{m}=a^{m+n}, m, n>0$,is

$y=f(x)$ and $x=g(y)$ are two curves and $P(x, y)$ is a common point of the two curves. If at $P$, on the curve $y=f(x)$, $\frac{dy}{dx}=Q(x)$ and at the same point $P$ on the curve $x=g(y)$, $\frac{dx}{dy}=-Q(x)$, then

If the tangent drawn at $A(2,1)$ to the curve $x=1+\frac{1}{y^2}$ meets the curve again at $B$,then

The sum of the intercepts on the coordinate axes made by the tangent to the curve $\sqrt{x} + \sqrt{y} = \sqrt{a}$ is