The lengths of tangent,subtangent,normal and subnormal for the curve $y=x^2+x-1$ at $(1,1)$ are $A, B, C$ and $D$ respectively,then their increasing order is

If the tangent to the curve $y=x+\sin y$ at a point $(a, b)$ is parallel to the line joining $\left(0, \frac{3}{2}\right)$ and $\left(\frac{1}{2}, 2\right),$ then

The coordinates of a point on the curve $x=a(\theta+\sin \theta), y=a(1-\cos \theta)$ where the tangent is inclined at an angle $\frac{\pi}{4}$ to the positive $X$-axis,are

Let the normal at a point $P$ on the curve $y^{2}-3x^{2}+y+10=0$ intersect the $y$-axis at $(0, \frac{3}{2})$. If $m$ is the slope of the tangent at $P$ to the curve,then $|m|$ is equal to

$P(5,2)$ is a point on the curve $y=f(x)$ and $\frac{7}{2}$ is the slope of the tangent to the curve at $P$. The area of the triangle (in sq. units) formed by the tangent and the normal to the curve at $P$ with the $x$-axis is:

If the equation of the tangent at $(2,3)$ on the curve $y^2 = ax^3 + b$ is $y = 4x - 5$,then the value of $a^2 + b^2$ is: