Show that the height of the cylinder of maximum volume, which can be inscribed in a sphere of radius R is  Also find the maximum volume.Â
Find the equation of the normal at a point on the curve x2 = 4y which passes through the point (1, 2). Also, find the equation of the corresponding tangent.
The equation of the given curve is x2 = 4y.
Differentiating w.r.t. x, we get
Let (h, k) be the co-ordinates of the point of contact of the normal to the curve x2 = 4y.
Now, slope of the tangent at (h, k) is given by
Hence, slope of the normal at (h, k) Â =Â
Therefore, the equation of normal at (h, k) isÂ
Since, it passes through the point (1, 2) we have
Now, (h, k) lies on the curve x2Â = 4y, so, we have:
            ...(3)Â
Solving (2) and (3), Â we get,
h = 2 Â and k = 1.
From (1), the required equation of the normal is:
Also, slope of the tangent  = 1
 Equation of tangent at (1, 2) is:
Find the Cartesian equation of the line passes through the point (-2, 4, -5) and is parallel to the lineÂ
The amount of pollution content added in air in city due to x-diesel vehicles is given by  Find the marginal increase in pollution content when 3 diesel vehicles are added and write which value is indicated in the above questions.