Hello, Columbo!

Find the derivative . . .Show that every tangent line to the curve

in the first quadrant has the property that the portion of the line

in the first quadrant has length 1, using implicit differentiation.

. .

Let be a point on the astroid in Quadrant 1.

. . Note that: .

The slope of the tangent at is: .

The equation of the line through with slope is:

. .

. . .

This tangent has: .x-intercept . . . and y-intercept

The length of that segment is: .

. .