A normal to the hyperbola, meets the co-ordinate axes x and y at A and B, respectively. If the parallelogram OABP ( O being the origin) is formed, then the locus of P is
Given hyperbola is
Equation of normal to (i) is given by
Coordinates of A are
and coordinates of
B are
Let the coordinates of P be (h, k). Since, diagonals of parallelogram bisect each other.
Squaring (ii) and (iii) and then subtracting, we get
Thus, locus of P is
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