Find a point `M` on the curve `y=3/(sqrt(2))\ \ xlnx ,\ x\ in (e^(-1. 5),\ oo)` such that the segment of the tangent at `M` intercepted between `M` and the Y-axis is shortest.

Find a point M on the curve y=(3)/(sqrt(2))x ln x,x in(e^(-1.5),oo) such that the segment of the tangent at M intercepted between M and the Y-axis is shortest.

Find all the curves y=f(x) such that the length of tangent intercepted between the point of contact and the x-axis is unity.

Find all the curves y=f(x) such that the length of tangent intercepted between the point of contact and the x-axis is unity.

Find the equation of a curve passing through the point (1, 1) , given that the segment of any tangent drawn to the curve between the point of tangency and the y-axis is bisected at the x-axis.

If m is the slope of the tangent to the curve e^(y)=1+x^(2) , then

If the slop of the tangent to the curve e^(y)=1x^(2) at any point is m. show that |m| le2 .

If m is the slope of the tangent to the curve, e^(y) =1 +x^(2) , then,

In the curve x^(m)y^(n)=k^(m+n)(m,n, k gt0) prove that the portion of the tangent intercepted between the coordinate axes is divided at its point of contact in a constant ratio,

The portion of tangent to curve x=√a^2-y^2 +- a/2 log a-√a^2-y^2 intercepted between curve and x axis is of length

Find the equation of tangents to the curve y = (x^(3) - 1) (x - 2) at the points, where the curve cuts the X-axis.