The coordinates of the point on the curve $y=x^2-3x+2$ where the tangent is perpendicular to the straight line $y=x$ are

$P(5,2)$ 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 $\theta$ is the angle between the curves $x^2-y^2=4$ and $y^2=3x$,then $\tan \theta=$

Find the coordinates of a point on the curve $y=x^2-3x+2$,at which the tangent drawn to this curve is perpendicular to the line $y=x$.

The equation of the tangent to the curve $y = b e^{-x / a}$ at the point where it crosses the $Y$ axis is

For the curve $xy = c^2$,the subnormal at any point varies as