Show that for the curve `b y^2=(x+a)^3,` the square of the sub-tangent varies as the sub-normal.

Prove that for the curve y=be^(x//a) , the subtangent is of constant length and the sub-normal varies as the square of the ordinate .

In the curve x^(m+n)=a^(m-n)y^(2n) , prove that the m t h power of the sub-tangent varies as the n t h power of the sub-normal.

A curve passing through (1, 0) is such that the ratio of the square of the intercept cut by any tangent on the y-axis to the Sub-normal is equal to the ratio of the product of the Coordinates of the point of tangency to the product of square of the slope of the tangent and the subtangent at the same point, is given by

In the curve y=c e^(x/a) , the sub-tangent is constant sub-normal varies as the square of the ordinate tangent at (x_1,y_1) on the curve intersects the x-axis at a distance of (x_1-a) from the origin equation of the normal at the point where the curve cuts y-a xi s is c y+a x=c^2

Show that equation to the curve such that the y-intercept cut off by the tangent at an arbitrary point is proportional to the square of the ordinate of the point of tangency is of the form a/x+b/y=1 .

Find the length of sub-tangent to the curve y=e^(x//a)

Show that A sub B then C- B sub C- A

For the curve y=a1n(x^2-a^2) , show that the sum of length of tangent and sub-tangent at any point is proportional to product of coordinates of point of tangency.

For the curve y=a1n(x^2-a^2) , show that the sum of length of tangent and sub-tangent at any point is proportional to product of coordinates of point of tangency.

For the curve y=f(x) prove that (lenght of normal)^2/(lenght of tangent)^2 =length of sub-normal/length of sub-tangent