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Intercept Form of a Line

Show that the...

Question

Show that the lines $2 x + 3 y + 19 = 0$ and $9 x + 6 y - 17 = 0$ cut the co-ordinate axes in concyclic points.

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Solution

A, B, C, D lie on same circle.
$O A \cdot O B = O C \cdot O D$
OAD & OCB are similar triangles.
The lengths OA, OB, OC, OD are straight towards to compute by setting $x = 0$
or $y = 0$ in equation of given lines.
Since,
$3 \times 6 = 2 \times 9$
The lines $2 x + 3 y + 19 = 0$ & $9 x + 6 y - 17 = 0$
meet the coordinates axis at concyclic points.

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