Let the normal at any point of hyperbola \(\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1\) intersect the coordinate axes at points P and Q. Then the locus of the mid-point of PQ is:
1
2(b2x2 + a2y2) = a2 + b2
2
2(b2x2 - a2y2) = a2 + b2
3
4(a2x2 + b2y2) = (a2 + b2)2
4
4(a2x2 - b2y2) = (a2 + b2)2