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 slope of tangent to the curve x^2 +y^2 = a^2/2

Prove that the portion of the tangent to the curve (x+sqrt(a^2-y^2))/a=(log)_e(a+sqrt(a^2-y^2))/y intercepted between the point of contact and the x-axis is constant.

The locus of the midpoints of the portion of the normal to the parabola y^(2)=16x intercepted between the curve and the axis is another parabola whose latus rectum is ___________ .

Find the locus of the midpoints of the portion of the normal to the parabola y^2=4a x intercepted between the curve and the axis.

Find the locus of the midpoints of the portion of the normal to the parabola y^2=4a x intercepted between the curve and the axis.

If length of tangent at any point on the curve y=f(x) intercepted between the point and the x-axis is of length 1 . Find the equation of the curve.

lf length of tangent at any point on th curve y=f(x) intercepted between the point and the x-axis is of length 1. Find the equation of the curve.

Prove that the length of segment of all tangents to curve x^(2/3)+y^(2/3)=a^(2/3) intercepted betweern coordina axes Is same and equal to =

If the length of the portion of the normal intercepted between a curve and the x-axis varies as the square of the ordinate, find the equation of the curve.

Find the equation of tangent of the curve x=at^(2), y = 2at at point 't'.