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 :
As we learned,
Path followed by a point p(x,y) under given condition (s).
It is satisfied by all the points (x,y) on the locus.
Mid-point formula -
If the point P(x,y) is the mid point of line joining A(x1,y1) and B(x2,y2) .
be point of contact.
Slope of normal =
line intersects X axis at A when y = 0
midpoint of OB =
midpoint of AP =
Put in Hyperbola , we get