Got kind of stuck on this question.
Suppose a is a non-zero constant. x^2/3+y^2/3=a^2/3. Show that the length of the portion of any tangent line to this astroid cut off by the x and y axes is constant.
I've differentiated implicitly to obtain the gradient of the tangent as And have obtained the equation of the tangent line passing through (q,0) and (0,p) as y=-(y/x)^1/3.x+p.
But how do i show that the length of this line passing through (q,0) and (0,p) is constant?
Thanks in advance.