If we can break the left-hand members of (1) into two factors, each of the first degree, then it will represent two straight lines.
If a be not zero, multiply equation (1) by a and arrange in powers oi x; it then becomes
On completing the square on the left hand we have
From (2) we cannot obtain x in terms of y, involving only terms of the first degree, unless the quantity under the radical sign be a perfect square.
The condition for this is
Cancelling and dividing by a, we have the required condition, viz.
