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The line lx + my + n = 0 intersects the curve

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The line lx + my + n = 0 intersects the curve ax2 + 2hxy + by2 = 1 at P and Q the circle with PA as diameter passes through the origin then (l2 + m2/n2).

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Let the circle passes through O(0, 0), P(x1​, x2​) and Q(y1​, y2​)

Now,

ax2 + 2hxy + by2 = 1

lx + my + n = 0

Since PQ is diameter and OP is perpendicular to OQ.

We have,

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