Consider the family of circles . If in the first quadrant, the common tangent to a circle of this family and the ellipse
meets the coordinate axes at A and B, then the equation of the locus of the mid-point of AB is,
...[1]
...[2]
are identical
The line (1) meets the coordinate axes at A(r secθ, 0) and
B(0, r cosecθ).
Let (h, k) be mid point of AB.
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