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,
Locus -
Path followed by a point p(x,y) under given condition (s).
- wherein
It is satisfied by all the points (x,y) on the locus.
and
Mid-point formula -
- wherein
If the point P(x,y) is the mid point of line joining A(x1,y1) and B(x2,y2) .
Given Hyperbola
be point of contact.
Slope of normal =
equation
line intersects X axis at A when y = 0
midpoint of OB =
midpoint of AP =
Thus
Put in Hyperbola , we get
Option 1)
Option 2)
Option 3)
Option 4)
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